Question

If each leg of a 45°-45°-90° triangle measures 8 centimeters, what is the perimeter of the triangle?

Answer 1

The perimeter of the triangle is 16 centimeters + 8√2 centimeters.

Step-by-step explanation:

A 45°-45°-90° triangle is a special type of right triangle where the two acute angles are equal. In this type of triangle, the length of the hypotenuse is equal to the length of one of the legs multiplied by √2. So, in this case, if each leg measures 8 centimeters, the length of the hypotenuse is 8√2 centimeters.

To find the perimeter of the triangle, we need to add the lengths of all three sides. So, the perimeter is 8 centimeters + 8 centimeters + 8√2 centimeters.

The sum of the two legs is 8 + 8 = 16 centimeters. Therefore, the perimeter of the triangle is 16 centimeters + 8√2 centimeters.

Answer 2

The perimeter is around 27 centimeters.

Step-by-step explanation:

Givens

• Each leg is 8 centimeters long.
• The angles of the right triangle are 45°, 45° and 90
• °.

Remember that the perimeter is the sum of all sides. So, we just need to find the hypothenuse using Pitagorean's Theorem.

`h^(2)=8^(2) +8^(2)\\ h=√(64+64)=√(128) \approx 11`

The perimeter would be

`P=8+8+11\\P=27`

Therefore, the perimeter is around 27 centimeters.