PYTHAGOREAN THEOREM WORD PROBLEMS WORKSHEET

About "Pythagorean theorem word problems worksheet"

Pythagorean theorem word problems worksheet :

Worksheet given in this section is much useful to the students who would like to practice solving word problems on "Pythagorean theorem". 

The Pythagorean theorem

In any right angle triangle, square of the hypotenuse is equal to sum of the squares of other two sides. 

That is,

 a² + b²  =  c²

Pythagorean theorem word problems worksheet - Problems

1. If the height of a triangle is 17 inches less than the length of its base and the length of the hypotenuse is 25 inches, find the base and the height.

2. The sides of an equilateral triangle are shortened by 12 units, 13 units, 14 units respectively and a right angle triangle is formed. Find the length of side of the equilateral triangle. 

3. If the sum of the lengths of two sides of a right triangle is 49 inches and the hypotenuse is 41 inches,then find the two sides.

4. From a train station, one train heads north, and another heads east. Some time later, the northbound train has traveled 12 miles, and the eastbound train has traveled 16 miles. How far apart are the two trains, measured in a straight line ?

5. The foot of a ladder is placed 6 feet from a wall. If the top of the ladder rests 8 feet up on the wall, how long is the ladder ? 

Pythagorean theorem word problems worksheet - Solution

Problem 1 : 

If the height of a triangle is 17 inches less than the length of its base and the length of the hypotenuse is 25 inches, find the base and the height.

Solution :

Let "x" be the length of the base.

Then, the height  =  x - 17

Hypotenuse  =  25

According to Pythagorean theorem, the square of the hypotenuse is equal to sum of the squares of other two sides.

So, we have ,  x² + (x-7)²   =   25²

x² + x² - 2(x)(17) + 17²  =  625 

2x² - 34x + 289   =   625

2x² - 34x - 336   =   0

x² -17x - 168   =   0

(x+7) (x-24)   =  0

x = -7  or  x = 24

x = -7 can not be accepted. (Because length can never be negative)

Then the length of the base ----> x  =  24 inches 

The length of the height is

x - 17  =  24 - 17  =  7 inches

Let us look at the next problem on "Pythagorean theorem word problems worksheet".

Problem 2  : 

The sides of an equilateral triangle are shortened by 12 units, 13 units, 14 units respectively and a right angle triangle is formed. Find the length of side of the equilateral triangle. 

Solution :

Let "x" be the length of side of the equilateral side. 

The sides of an equilateral triangle are shortened by 12 units, 13 units, 14 units and a right angle triangle is formed.  

Then, new lengths are  (x-12), (x-13) and (x-14)

These are the sides of a right angle triangle. 

And also hypotenuse = (x-12)

Because (x-12) is the longest side. 

According to Pythagorean theorem, the square of the hypotenuse is equal to sum of the squares of other two sides.

So, we have ,  (x - 13)² + (x - 14)²   =   (x - 12)²

x² - 2(x)(13) + 13² + x² - 2(x)(14) + 14² = x² - 2(x)(12) + 144

x² - 26x + 169 + x² - 28x + 196 = x² - 24x + 144

2x² - 54x + 365  =  x² - 24x + 144

 x² - 30x + 221   =   0

(x - 13)(x - 17)   =   0

x  =  13  or x  =  17

If we take x = 13, the sides of the right triangle are

x - 12 = 1,   x - 13 = 0,  x - 14 = -1

When x = 13, we get one of the sides is zero and the sign of the another side is negative.  

So, x = 13 can not be accepted.

If we take x = 17, the sides of the right triangle are

x - 12 = 5,   x - 13 = 4 ,  x - 14 = 3

All of the three sides of the right angle are positive when x = 17. 

So, x = 17 can be accepted. 

Hence, the length of side of equilateral triangle is 17 units. 

Let us look at the next problem on "Pythagorean theorem word problems worksheet".

Problem 3  : 

If the sum of the lengths of two sides of a right triangle is 49 inches and the hypotenuse is 41 inches,then find the two sides.

Solution :

Let "x" be one of the two sides. 

Given : Sum of the two sides = 49

Then the length of other side = 49 - x

And also hypotenuse = 41

According to Pythagorean theorem, the square of the hypotenuse is equal to sum of the squares of other two sides.

So, we have ,  x² + (49 - x)²   =   41²

x² + 49² - 2(49)(x) + x²  =  1681 

2x² - 98x + 2401   =   1681

2x² - 98x + 720  =   0

x² - 49x + 360   =   0

(x-40) (x-9)   =  0

x = 40  or  x = 9

If x = 40, then the length of other side is

49 - x  =  49 - 40  =  9

If x = 9, then the length of other side is

49 - x  =  49 - 9  =  40

Hence, the lengths of other two sides are 9 inches and 40 inches. 

Let us look at the next problem on "Pythagorean theorem word problems worksheet".

Problem 4  : 

From a train station, one train heads north, and another heads east. Some time later, the northbound train has traveled 12 miles, and the eastbound train has traveled 16 miles. How far apart are the two trains, measured in a straight line ?

Solution :

Let "x" be the required distance. 

According to Pythagorean theorem, the square of the hypotenuse is equal to sum of the squares of other two sides.

So, we have ,  12² + 16²   =   x²

144 + 256  =  x²  

400   =   x²

20²  =  x²

20  =  x

Hence, the distance between the two trains is 20 miles. 

Let us look at the next problem on "Pythagorean theorem word problems worksheet".

Problem 5  : 

The foot of a ladder is placed 6 feet from a wall. If the top of the ladder rests 8 feet up on the wall, how long is the ladder? 

Solution : 

Let "x" be the required distance. 

According to Pythagorean theorem, the square of the hypotenuse is equal to sum of the squares of other two sides.

So, we have ,  8² + 6²   =   x²

64 + 36  =  x²  

100   =   x²

10²  =  x²

10  =  x

Hence, the length of the ladder is 10 feet. 

After having gone through the stuff given above, we hope that the students would have understood "Pythagorean theorem word problems worksheet". 

Apart from the stuff given above, if you want to know more about "Pythagorean theorem word problems worksheet", please click here

Apart from the stuff given on "Pythagorean theorem word problems worksheet", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

ALGEBRA

Variables and constants

Writing and evaluating expressions

Solving linear equations using elimination method

Solving linear equations using substitution method

Solving linear equations using cross multiplication method

Solving one step equations

Solving quadratic equations by factoring

Solving quadratic equations by quadratic formula

Solving quadratic equations by completing square

Nature of the roots of a quadratic equations

Sum and product of the roots of a quadratic equations 

Algebraic identities

Solving absolute value equations 

Solving Absolute value inequalities

Graphing absolute value equations  

Combining like terms

Square root of polynomials 

HCF and LCM 

Remainder theorem

Synthetic division

Logarithmic problems

Simplifying radical expression

Comparing surds

Simplifying logarithmic expressions

Negative exponents rules

Scientific notations

Exponents and power

COMPETITIVE EXAMS

Quantitative aptitude

Multiplication tricks

APTITUDE TESTS ONLINE

Aptitude test online

ACT MATH ONLINE TEST

Test - I

Test - II

TRANSFORMATIONS OF FUNCTIONS

Horizontal translation

Vertical translation

Reflection through x -axis

Reflection through y -axis

Horizontal expansion and compression

Vertical  expansion and compression

Rotation transformation

Geometry transformation

Translation transformation

Dilation transformation matrix

Transformations using matrices

ORDER OF OPERATIONS

BODMAS Rule

PEMDAS Rule

WORKSHEETS

Converting customary units worksheet

Converting metric units worksheet

Decimal representation worksheets

Double facts worksheets

Missing addend worksheets

Mensuration worksheets

Geometry worksheets

Comparing  rates worksheet

Customary units worksheet

Metric units worksheet

Complementary and supplementary worksheet

Complementary and supplementary word problems worksheet

Area and perimeter worksheets

Sum of the angles in a triangle is 180 degree worksheet

Types of angles worksheet

Properties of parallelogram worksheet

Proving triangle congruence worksheet

Special line segments in triangles worksheet

Proving trigonometric identities worksheet

Properties of triangle worksheet

Estimating percent worksheets

Quadratic equations word problems worksheet

Integers and absolute value worksheets

Decimal place value worksheets

Distributive property of multiplication worksheet - I

Distributive property of multiplication worksheet - II

Writing and evaluating expressions worksheet

Nature of the roots of a quadratic equation worksheets

Determine if the relationship is proportional worksheet

TRIGONOMETRY

SOHCAHTOA

Trigonometric ratio table

Problems on trigonometric ratios

Trigonometric ratios of some specific angles

ASTC formula

All silver tea cups

All students take calculus 

All sin tan cos rule

Trigonometric ratios of some negative angles

Trigonometric ratios of 90 degree minus theta

Trigonometric ratios of 90 degree plus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 180 degree minus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 270 degree minus theta

Trigonometric ratios of 270 degree plus theta

Trigonometric ratios of angles greater than or equal to 360 degree

Trigonometric ratios of complementary angles

Trigonometric ratios of supplementary angles 

Trigonometric identities 

Problems on trigonometric identities 

Trigonometry heights and distances

Domain and range of trigonometric functions 

Domain and range of inverse  trigonometric functions

Solving word problems in trigonometry

Pythagorean theorem

MENSURATION

Mensuration formulas

Area and perimeter

Volume

GEOMETRY

Types of angles 

Types of triangles

Properties of triangle

Sum of the angle in a triangle is 180 degree

Properties of parallelogram

Construction of triangles - I 

Construction of triangles - II

Construction of triangles - III

Construction of angles - I 

Construction of angles - II

Construction angle bisector

Construction of perpendicular

Construction of perpendicular bisector

Geometry dictionary

Geometry questions 

Angle bisector theorem

Basic proportionality theorem

ANALYTICAL GEOMETRY

Analytical geometry formulas

Distance between two points

Different forms equations of straight lines

Point of intersection

Slope of the line 

Perpendicular distance

Midpoint

Area of triangle

Area of quadrilateral

Parabola

CALCULATORS

Matrix Calculators

Analytical geometry calculators

Statistics calculators

Mensuration calculators

Algebra calculators

Chemistry periodic calculator

MATH FOR KIDS

Missing addend 

Double facts 

Doubles word problems

LIFE MATHEMATICS

Direct proportion and inverse proportion

Constant of proportionality 

Unitary method direct variation

Unitary method inverse variation

Unitary method time and work

SYMMETRY

Order of rotational symmetry

Order of rotational symmetry of a circle

Order of rotational symmetry of a square

Lines of symmetry

CONVERSIONS

Converting metric units

Converting customary units

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

Word problems on comparing rates

Converting customary units word problems 

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles 

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed 

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6

HTML Comment Box is loading comments...