Question

If triangle DEF has sides measuring 50, 40, and 32, is the triangle a right triangle?

1) 90
2) 0

Answer 1

By applying the Pythagorean theorem, it was determined that triangle DEF with sides measuring 50, 40, and 32 does not fulfill the condition for being a right triangle. The squares of the side lengths do not add up correctly, confirming that triangle DEF is not a right triangle.

Step-by-step explanation:

To determine if triangle DEF with sides measuring 50, 40, and 32 is a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

We will compare the squares of the side lengths:
502 = 2500
402 = 1600
322 = 1024

If this is a right triangle, the sum of the squares of the two shorter sides should be equal to the square of the longest side. So, we check if 402 + 322 = 502:

1600 + 1024 = 2624
2500 = 2500

Since 2624 ≠ 2500, the sides do not satisfy the Pythagorean theorem, and therefore, triangle DEF is not a right triangle.