Question

Question

If triangle DEF
has sides measuring 50, 40, and 32, is the triangle a right triangle? If it is a right triangle, answer with the number 90. If it is not a right triangle, answer with the number 0.(1 point)

Answer 1

To determine if triangle DEF is a right triangle, we can use the Pythagorean theorem. The sides of the triangle are 50, 40, and 32.

The Pythagorean theorem states that for a triangle with sides $a$, $b$, and $c$ (where $c$ is the longest side), the triangle is a right triangle if:

$$a^2+b^2=c^2$$

Here, let's assign:

• $c=50$ (the longest side)
• $a=40$
• $b=32$

Now we will calculate $a^2+b^2$ and $c^2$:

$$a^2+b^2={40}^2+{32}^2=1600+1024=2624$$ $$c^2={50}^2=2500$$

Now we compare $a^2+b^2$ and $c^2$:

$$2624\ne 2500$$

Since $a^2+b^2$ does not equal $c^2$, triangle DEF is not a right triangle. Therefore, the answer is:

$$0$$