SOLUTION: The shortest side of a right triangle measures 7m. the lengths of the other two sides are consecutive integers, the hypotenuse being the longer of the two. find the lengths of the

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Question 1019582: The shortest side of a right triangle measures 7m. the lengths of the other two sides are consecutive integers, the hypotenuse being the longer of the two. find the lengths of the other two sides. Please show all work to find the answer.
Answer by ikleyn(52873) About Me  (Show Source):
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The shortest side of a right triangle measures 7m. the lengths of the other two sides are consecutive integers,
the hypotenuse being the longer of the two. find the lengths of the other two sides. Please show all work to find the answer.
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Answer. 7, 24, 25. 

Solution

Let x be the length of the hypotenuse,
Then the length of the longer leg is x-1, according to the condition.

The Pythagorean equation is 

7%5E2+%2B+%28x-1%29%5E2 = x%5E2.

Simplify and solve it, and you will get the answer.