MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The hypotenuse of an isosceles right triangle is 6 units long. Find the exact values of the perimeter P and area A of the triangle.

Answer 1

If it's an isosceles right triangle then a picture would look like this:

Notice the two legs are the same but since we don't know what they are, we can label them "x".

Since it's a right triangle, we can use the Pythagorean Theorem:

a² + b² = c² or in this case:

x² + x² = 6²

2x² = 36

x² = 18

x = √18 = √(9•2) = √9•√2 = 3√2

The perimeter is the sum of all the sides = 6 + 3√2 + 3√2 = 6 + 6√2 units

The area is calculated from A = (1/2)bh = (1/2)(3√2)(3√2) = (1/2)(3•3)(√2•√2) = (1/2)(9)(2) = 9 square units