# High School Math : How to find the length of the hypotenuse of a 45/45/90 right isosceles triangle : Pythagorean Theorem

## Example Questions

### Example Question #1 : 45/45/90 Right Isosceles Triangles

In an isosceles right triangle, two sides equal . Find the length of side

Possible Answers:

Correct answer:

Explanation:

This problem represents the definition of the side lengths of an isosceles right triangle.  By definition the sides equal , and .  However, if you did not remember this definition one can also find the length of the side using the Pythagorean theorem .

### Example Question #2 : 45/45/90 Right Isosceles Triangles

ABCD is a square whose side is  units.  Find the length of diagonal AC.

Possible Answers:

none of the other answers

Correct answer:

Explanation:

To find the length of the diagonal, given two sides of the square, we can create two equal triangles from the square. The diagonal line splits the right angles of the square in half, creating two triangles with the angles of , , and  degrees. This type of triangle is a special right triangle, with the relationship between the side opposite the  degree angles serving as x, and the side opposite the  degree angle serving as .

Appyling this, if we plug  in for  we get that the side opposite the right angle (aka the diagonal) is

### Example Question #3 : 45/45/90 Right Isosceles Triangles

The area of a square is . Find the length of the diagonal of the square.

Possible Answers:

Correct answer:

Explanation:

If the area of the square is , we know that each side of the square is , because the area of a square is .

Then, the diagonal creates two special right triangles. Knowing that the sides = , we can find that the hypotenuse (aka diagonal) is