Given:
The figure of a right angle triangle.
[tex]a=b[/tex]
Hypotenuse = [tex]9\sqrt{2}[/tex] 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 [tex]9\sqrt{2}[/tex] in.
Using Pythagoras theorem, we get
[tex]Hyponteuse^2=Base^2+Perpendicular^2[/tex]
[tex](9\sqrt{2})^2=(a)^2+(b)^2[/tex]
[tex]81(2)=(a)^2+(a)^2[/tex] [tex][\because a=b][/tex]
[tex]81(2)=2(a)^2[/tex]
Divide both sides by 2.
[tex]81=(a)^2[/tex]
Taking square root on both sides.
[tex]\pm \sqrt{81}=a[/tex]
[tex]\pm 9=a[/tex]
Side cannot be negative. So,
[tex]9=a[/tex]
Thus, the missing side lengths are a=9 in and b=9 in.
Therefore, the correct option is C.