Question

Which of the following sets of numbers could represent the three sides of a right triangle?

21, 72, 75,
7, 8, 10
8, 12, 15
14, 84, 85

Answer 1

Answer: 21 , 72 , 75

Explanation:

The one that could represent the three sides of a right angle triangle must obey Pythagoras theorem , that is

`a^(2)+b^(2)=c^(2)`

a = side of right triangle

b = side of right triangle

c = hypotenuse

Let's check the sides one after the other

1.
`21 , 72 , 75`

`21^(2)+72^(2) = 5,625`

`75^(2)=5625`

this means that

`21^(2)+72^(2)=75^(2)`

this could represent the three sides of a right triangle

2.
`7,8,10`

`7^(2)+8^(2)=113`

`10^(2)=100`

`7^(2)+8^(2)\\eq 10^(2)`

3.
`8, 12 , 15`

`8^(2)+12^(2)= 208`

`15^(2)=225`

`8^(2)+12^(2)\\eq 15^(2)`

4.
`14,84,85`

`14^(2)+84^(2)=7,252`

`85^(2) = 7225`

`14^(2)+84^(2)\\eq 85^(2)`

Therefore , the only combination that could represent the three sides of a right triangle will be 21 , 72 , 75