# PSAT Math : 45/45/90 Right Isosceles Triangles

## Example Questions

### Example Question #7 : 45/45/90 Right Isosceles Triangles

An isosceles triangle has a base of 6 and a height of 4. What is the perimeter of the triangle?

None of these

Explanation:

An isosceles triangle is basically two right triangles stuck together. The isosceles triangle has a base of 6, which means that from the midpoint of the base to one of the angles, the length is 3. Now, you have a right triangle with a base of 3 and a height of 4. The hypotenuse of this right triangle, which is one of the two congruent sides of the isosceles triangle, is 5 units long (according to the Pythagorean Theorem).

The total perimeter will be the length of the base (6) plus the length of the hypotenuse of each right triangle (5).

5 + 5 + 6 = 16

### Example Question #8 : 45/45/90 Right Isosceles Triangles

What is the area of a square that has a diagonal whose endpoints in the coordinate plane are located at (-8, 6) and (2, -4)?

100√2

200√2

100

50

50√2