Question
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.
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.
Answers
GPT-4o mini
To determine whether triangle DEF with sides measuring 50, 40, and 32 is a right triangle, we can apply the Pythagorean theorem. According to this theorem, if a triangle is a right triangle, the square of the length of the longest side (hypotenuse) should be equal to the sum of the squares of the other two sides.
Let's assign the sides as follows:
- \( c = 50 \) (longest side)
- \( a = 40 \)
- \( b = 32 \)
Now we check if \( c^2 = a^2 + b^2 \):
\[
c^2 = 50^2 = 2500
\]
\[
a^2 + b^2 = 40^2 + 32^2 = 1600 + 1024 = 2624
\]
Now we compare the results:
\[
2500 \neq 2624
\]
Since \( c^2 \) does not equal \( a^2 + b^2 \), triangle DEF is not a right triangle.
Thus, the answer is \( \boxed{0} \).
Let's assign the sides as follows:
- \( c = 50 \) (longest side)
- \( a = 40 \)
- \( b = 32 \)
Now we check if \( c^2 = a^2 + b^2 \):
\[
c^2 = 50^2 = 2500
\]
\[
a^2 + b^2 = 40^2 + 32^2 = 1600 + 1024 = 2624
\]
Now we compare the results:
\[
2500 \neq 2624
\]
Since \( c^2 \) does not equal \( a^2 + b^2 \), triangle DEF is not a right triangle.
Thus, the answer is \( \boxed{0} \).