To determine if triangle DEF is a right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's calculate the squares of the lengths of the sides:
Length of side DE: 50^2 = 2500
Length of side EF: 40^2 = 1600
Length of side DF: 32^2 = 1024
Now, let's check if the sum of the squares of the two shorter sides is equal to the square of the longest side:
2500 + 1600 = 4100
Since 4100 is not equal to 1024, triangle DEF is not a right triangle. Therefore, the answer is 0.
Triangles Unit Test
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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)
3 answers
are u sure
Apologies, I made a mistake in my calculations. Let's correct it:
Length of side DE: 50^2 = 2500
Length of side EF: 40^2 = 1600
Length of side DF: 32^2 = 1024
Now, let's check if the sum of the squares of the two shorter sides is equal to the square of the longest side:
2500 + 1600 = 4100
4100 = 1024
Since 4100 is not equal to 1024, triangle DEF is not a right triangle. Therefore, the answer is 0.
Length of side DE: 50^2 = 2500
Length of side EF: 40^2 = 1600
Length of side DF: 32^2 = 1024
Now, let's check if the sum of the squares of the two shorter sides is equal to the square of the longest side:
2500 + 1600 = 4100
4100 = 1024
Since 4100 is not equal to 1024, triangle DEF is not a right triangle. Therefore, the answer is 0.