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

Answer:

Each leg is 8 units long

Step-by-step 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

$a=AC\\b=BC\\AC=BC\\c=AB=8\sqrt{2}\ units$

substitute

$(8\sqrt{2})^2=a^2+b^2$

$(8\sqrt{2})^2=2a^2$

$128=2a^2$

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

therefore

$AC=BC=8\ units$

Each leg is 8 units long