Question 101989: A triangle had the following side lengths: 33 ft, 56 ft and 65 ft. Was it a right triangle?
Explain. Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! If this is a right triangle, then the Pythagorean theorem applies. The Pythagorean theorem says
that in a right triangle the square of the length of the hypotenuse (the longest side) equals
the sum of the squares of the two remaining sides (called the legs). So if the triangle
is a right triangle the square of the longest side (65 ft) equals the sum of the square of the
shortest side (33 ft) plus the square to the remaining side (56 ft). In equation form this
becomes:
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If this equation is true, then the triangle is a right triangle.
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On the left side the square of 65 is 65 times 65 which is 4225. On the right side the
square of 33 is 33 times 33 which is 1089 and the square of 56 is 56 times 56 which is 3136.
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Substituting these values into the Pythagorean base equation results in:
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and adding the two numbers on the right side leads to the equation becoming:
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Since the Pythagorean equation is true for this triangle, the triangle is a right triangle.
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Hope this helps you to understand how you can do this problem.
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