# PSAT Math : How to find the perimeter of a 45/45/90 right isosceles triangle

## Example Questions

### Example Question #1 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

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

Possible Answers:

None of these

Correct answer:

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

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