Real World Problems on Pythagorean Theorem :
Here we are going to see some practice problems on pythagorean theorem.
Question 1 :
A man goes 18 m due east and then 24 m due north. Find the distance of his current position from the starting point?
the distance of his current position from the starting point = √182 + 242
= √(324 + 576)
= 30 m
Hence the required distance is 30 m.
Question 2 :
There are two paths that one can choose to go from Sarah’s house to James house. One way is to take C street, and the other way requires to take A street and then B street. How much shorter is the direct path along C street? (Using figure).
By choosing the C street, he has to cover the distance,
= √22 + 1.52
= √(4 + 2.25)
= 2.5 miles
By choosing the alternative way, he has to cover the distance = 2 + 1.5
= 3.5 miles
The difference between these two paths = 3.5 - 2.5
= 1 mile
Hence by choosing the direct path, he may save 1 miles faster than other way.
Question 3 :
To get from point A to point B you must avoid walking through a pond. You must walk 34 m south and 41 m east. To the nearest meter, how many meters would be saved if it were possible to make a way through the pond?
By drawing the rough picture using the given information, we get
AC = √342 + 412
= √1156 + 1681
Miles saved = (34 + 41) - 53.26
= 75 - 53.26
= 21.74 m
Question 4 :
In the rectangle WXYZ, XY + YZ = 17 cm, and XZ + YW = 26 cm. Calculate the length and breadth of the rectangle?
XY + YZ = 17 cm
XZ + YW = 26 cm
To calculate : - Length and breadth of the rectangle.
We know that,
Diagonals of a rectangle are equal.
So, XZ = YW
Then, XZ = YW = 26/2 = 13 cm
In ∆XYZ ,
Let YZ = P , Then, XY = (17 - P).
Then, by Pythagoras theorem,
(P)² + (17 - P)² = (13)²
P² + 289 - 34P + P² = 169
2P² - 34P = 169 - 289
2(P² - 17P) = - 120
P² - 17P = - 120/2
P² - 17P = - 60
P² - 17P + 60 = 0
P² - 12P - 5P + 60 = 0
P(P - 12) - 5(P - 12) = 0
(P - 12)(P - 5) = 0
P - 12 = 0, P = 12
P = 12 cm
P - 5 = 0 => P = 5 cm
YZ = P = 12 cm [Because , YZ is the length of the rectangle ,so we will assign it the greatest value of P]
Again, XY = (17 - P) = (17 - 12) cm = 5 cm
[Because , XY is thee breadth.]
After having gone through the stuff given above, we hope that the students would have understood, "Real World Problems on Pythagorean Theorem".
Apart from the stuff given in this section "Real World Problems on Pythagorean Theorem", if you need any other stuff in math, please use our google custom search here.
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
Area and perimeter worksheets
Decimal place value worksheets
Area and perimeter
Different forms equations of straight lines
MATH FOR KIDS
HCF and LCM word problems
Word problems on simple equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on comparing rates
Ratio and proportion word problems
Converting repeating decimals in to fractions