Find AC in Isosceles Triangle ABC with Sides 80 and 20

To solve for the hypotenuse $AC$ in triangle $\triangle ABC$, we'll use the Pythagorean theorem:

• Step 1: Identify sides: In the isosceles right triangle, let $AB = 80$, $BC = 20$. These are the two legs.
• Step 2: Substitute into the Pythagorean theorem: $AB^2 + BC^2 = AC^2$.
• Step 3: Perform calculations:

Substitute the values into the equation:
$80^2 + 20^2 = AC^2$.

Calculate each square value:
$6400 + 400 = AC^2$.

Combine the values:
$6800 = AC^2$.

To solve for $AC$, take the square root of both sides:
$AC = \sqrt{6800}$.

Therefore, the solution for the length of $AC$ is $\sqrt{6800}$.