Question

In the right triangle shown, AC = BC and AB = 8V2.

How long are each of the legs?
Answer exactly, using a radical if needed.

Answer 1

Each leg is 8 units long

Explanation:

see the attached figure to better understand the problem

we know that

Any right triangle must satisfy the Pythagorean Theorem

so

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

where

c is the hypotenuse (greater side)

a and b are the legs (perpendicular sides)

In this problem we have

`a=AC\\b=BC\\AC=BC\\c=AB=8√(2)\ units`

substitute

`(8√(2))^2=a^2+b^2`

`(8√(2))^2=2a^2`

`128=2a^2`

`a^2=64\\a=8\ units`

therefore

`AC=BC=8\ units`

Each leg is 8 units long