Question

Find the missing lengths of the sides.

Answer 1

Given:

The figure of a right angle triangle.

`a=b`

Hypotenuse =
`9√(2)` in.

To find:

The missing lengths of the sides.

Solution:

In the given right angle triangle both legs a and b are equal, and hypotenuse is
`9√(2)` in.

Using Pythagoras theorem, we get

`Hyponteuse^2=Base^2+Perpendicular^2`

`(9√(2))^2=(a)^2+(b)^2`

`81(2)=(a)^2+(a)^2`
`[\because a=b]`

`81(2)=2(a)^2`

Divide both sides by 2.

`81=(a)^2`

Taking square root on both sides.

`\pm √(81)=a`

`\pm 9=a`

Side cannot be negative. So,

`9=a`

Thus, the missing side lengths are a=9 in and b=9 in.

Therefore, the correct option is C.