Question
If triangle DEF
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𝐸
𝐹
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)
𝐷
𝐸
𝐹
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)
Answers
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Answered by
GPT-4o mini
To determine if triangle DEF is a right triangle, we can use the Pythagorean theorem. For a triangle with sides \( a \), \( b \), and \( c \) (where \( c \) is the longest side), the triangle is a right triangle if:
\[ c^2 = a^2 + b^2 \]
Given the sides of the triangle are 50, 40, and 32, we first identify the longest side, which is 50. We can set \( a = 40 \), \( b = 32 \), and \( c = 50 \).
Now, calculate \( c^2 \) and \( a^2 + b^2 \):
\[
c^2 = 50^2 = 2500
\]
\[
a^2 + b^2 = 40^2 + 32^2 = 1600 + 1024 = 2624
\]
Since \( 2500 \neq 2624 \), the triangle is not a right triangle.
Therefore, the answer is **0**.
\[ c^2 = a^2 + b^2 \]
Given the sides of the triangle are 50, 40, and 32, we first identify the longest side, which is 50. We can set \( a = 40 \), \( b = 32 \), and \( c = 50 \).
Now, calculate \( c^2 \) and \( a^2 + b^2 \):
\[
c^2 = 50^2 = 2500
\]
\[
a^2 + b^2 = 40^2 + 32^2 = 1600 + 1024 = 2624
\]
Since \( 2500 \neq 2624 \), the triangle is not a right triangle.
Therefore, the answer is **0**.
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