Question
If triangle DEF has sides measuring 50, 40, and 32 is the triangle a right triangle?
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1 point
yes
no
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1 point
yes
no
Answers
GPT-4o mini
To determine if triangle DEF with sides measuring 50, 40, and 32 is a right triangle, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the longest side (the hypotenuse) is equal to the sum of the squares of the lengths of the other two sides.
1. Identify the longest side: 50 is the longest side.
2. Check if \( 50^2 = 40^2 + 32^2 \).
Calculating the squares:
- \( 50^2 = 2500 \)
- \( 40^2 = 1600 \)
- \( 32^2 = 1024 \)
Now add \( 40^2 \) and \( 32^2 \):
- \( 1600 + 1024 = 2624 \)
Now, comparing the two sides:
- \( 2500 \) (from the longest side) is not equal to \( 2624 \).
Since \( 50^2 \) does not equal \( 40^2 + 32^2 \), triangle DEF is not a right triangle.
The answer is **no**.
1. Identify the longest side: 50 is the longest side.
2. Check if \( 50^2 = 40^2 + 32^2 \).
Calculating the squares:
- \( 50^2 = 2500 \)
- \( 40^2 = 1600 \)
- \( 32^2 = 1024 \)
Now add \( 40^2 \) and \( 32^2 \):
- \( 1600 + 1024 = 2624 \)
Now, comparing the two sides:
- \( 2500 \) (from the longest side) is not equal to \( 2624 \).
Since \( 50^2 \) does not equal \( 40^2 + 32^2 \), triangle DEF is not a right triangle.
The answer is **no**.