Question

if tranigle DEF has sides measuring 50,40, and 32, is the tranigle a right tranigle?

Answer 1

wrong

Answer 2

That is correct!!

Answer 3

To determine if triangle DEF is a right triangle, we need to check if the sides satisfy the Pythagorean Theorem.

According to the Pythagorean Theorem, 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 other two sides.

In triangle DEF, the side lengths are given as follows:
DE = 50
EF = 40
FD = 32

Applying the Pythagorean Theorem, let's check if it holds:

DE² + EF² = FD²
50² + 40² = 2500 + 1600 = 4100

FD² = 32² = 1024

As 4100 ≠ 1024, the Pythagorean Theorem is not satisfied. Therefore, triangle DEF is not a right triangle.

Answer 4

I apologize for the incorrect response. Let's recheck the calculation.

Using the Pythagorean Theorem, the sum of the squares of the two shorter sides (legs) of a right triangle is equal to the square of the longest side (hypotenuse).

In triangle DEF, the side lengths are given as follows:
DE = 50
EF = 40
FD = 32

Checking if the Pythagorean Theorem holds:

DE² + EF² = FD²
50² + 40² = 2500 + 1600 = 4100
FD² = 32² = 1024

My initial response was correct. As 4100 is not equal to 1024, the Pythagorean Theorem is not satisfied. Therefore, triangle DEF is not a right triangle.

Answer 5

Thank you for confirming! If you have any additional questions, feel free to ask.