Question

Find the missing lengths of the sides.

Answer 1

Given:

The figure of a right angle triangle.

$a=b$

Hypotenuse = $9\sqrt{2}$ 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 $9\sqrt{2}$ in.

Using Pythagoras theorem, we get

$Hyponteuse^2=Base^2+Perpendicular^2$

$(9\sqrt{2})^2=(a)^2+(b)^2$

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

$81(2)=2(a)^2$

Divide both sides by 2.

$81=(a)^2$

Taking square root on both sides.

$\pm \sqrt{81}=a$

$\pm 9=a$

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.