## SOLVING WORD PROBLEMS INVOLVING THE SHAPES SQUARES AND RECTANGLES

Problem 1 :

The side of a square exceeds the side of another square by 4 cm and the sum of the area of two squares is 400 sq.cm. Find the dimensions of the squares.

Solution :

Let x be side length of one square

The side of a square exceeds the side of another square by 4 cm

So, the side length of another square  =  x + 4

Area of one square with side length x  =  x2

Area of one square with side length x + 4 is (x + 4)²

Sum of the area of two squares  =  400 sq.cm

x2 + (x + 4)2  =  400

x2 + x2 + 2 ⋅  4 + 42  =  400

2x2 + 8x + 16 - 400  =  0

2x2 + 8x - 384  =  0

By dividing the entire equation by 2, we get

x2 + 4x - 192  =  0

(x + 16) (x - 12) = 0

 x + 16  =  0x  =  -16 x - 12  =  0x  =  12

Therefore sides of one square is 12 cm.

Side length of another square  =  (12 + 4)  =  16 cm.

Problem 2 :

The length of the rectangle exceeds its width by 2 cm and the area of the rectangle is 195 sq.cm. Find the dimensions of the rectangle.

Solution :

Let x and y be the width and length of rectangle respectively

The length of the rectangle exceeds its width by 2 cm

So, length (y)  =  x + 2

Area of the rectangle  =  195 sq.cm

Length  width = 195

x(x + 2)  =  195

x2 + 2x - 195  =  0

(x + 15) (x - 13)  =  0

 x + 15  =  0x  =  -15 x - 13  =  0x  =  13

Here x represents width of the rectangle. So, the negative value is not possible.

To find the value of y we have to apply the value of x in the equation y = x + 2

y  =  13 + 2

y  =  15 cm

Therefore length of rectangle is 15 cm and width of the rectangle is 13 cm.

Problem 3 :

The footpath of uniform width runs all around a rectangular field 28 meters long and 22 meters wide. If the path occupies 600 m² area, find the width of the path.

Solution :

Let x be the width of the path

Length of the rectangular field  =  28 m

Width of the rectangular field  =  22 m

Area of the path  =  600 m2

Length of the larger rectangle :

=  28 + x + x

=  28 + 2x

Width of the larger rectangle :

=  22 + x + x

=  22 + 2x

Area of the path  =  Area of larger rectangle - Area of smaller rectangle

600  =  (28 + 2x)  (22 + 2x) - 28  22

600  =  616 + 56x + 44x + 4x2 - 616

600  =  56x + 44x + 4x2

600  =  4x2 + 100 x

4x² + 100x  =  600

Dividing the entire equation by 4, we get

x+ 25x  =  150

x² + 25x - 150  =  0

(x - 5) (x + 30)  =  0

 x - 5  =  0x  =  5 x + 30  =  0x  =  -30

Negative value is not possible. Because x represents width of the path.

Therefore width of the path is 5 m

Apart from the stuff given on this web page, if you need any other stuff in math, please use our google custom search here

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear 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