Question

In the right triangle shown, AC = BCAC=BCA, C, equals, B, C and AB = 12\sqrt{2}AB=12 2 ​ A, B, equals, 12, square root of, 2, end square root. How long are each of the legs?

Answer 1

AC= 18 units for khan academy

Explanation:

Answer 2

Given:

ABC is a right triangle and AC = BC

The length of AB is
`AB=12√(2)`

We need to determine the length of each of the legs.

Length of AC and BC:

Let the length of AC and BC be x.

The length of AC and BC can be determined using the Pythagorean theorem.

Thus, we have;

`AB^2=AC^2+CB^2`

Substituting the values, we have;

`(12√(2))^2=x^2+x^2`

Simplifying, we get;

`288=2x^2`

Dividing both sides by 2, we get;

`144=x^2`

Taking square root on both sides, we get;

`12=x`

Thus, the length of each legs is 12 units.

Hence, the length of AC and BC are 12 units each.