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 \( c^2 \):

\[
2624 \neq 2500
\]

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

\[
0
\]