Question

One side of a right triangle has a length of 24 centimeters. What could be the lengths of the other two sides of the right triangle?

A.
7 centimeters and 25 centimeters
B.
8 centimeters and 23 centimeters
C.
9 centimeters and 22 centimeters
D.
10 centimeters and 27 centimeters

Answer 1

A. 7 centimetres and 25 centimetres

Explanation:

To see if the lengths make a triangle, use the Pythagorean theorem. Insert the biggest value as c (the hypotenuse, which is always the longest side in a right triangle). If both sides equal each other, it is a right triangle:

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

A.

`24^2+7^2=25^2\\\\576+49=625\\\\625=625`

This is a right triangle.

B.

`23^2+8^2=24^2\\\\529+64=576\\\\593\\eq 576`

Not a right triangle.

C.

`9^2+22^2=24^2\\\\81+484=576\\\\565\\eq 576`

Not a right triangle.

D.

`24^2+10^2=27^2\\\\576+100=729\\\\676\\eq 729`

Not a right triangle.

Done :D