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One leg of a right triangle has a length of 77 m. the other sides have lengths that are consecutive integers. find these lengths.

User Robot
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1 Answer

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Let x and x+1 represent the consecutive integers, then x is the other leg and x+1 is the hypotenuse (because the hypotenuse must be greater than its sides).

Use Pythagorean Theorem:
a² + b² = c²
(77)² + x² = (x+1)²
5929 + x² = x² + 2x + 1
5928 = 2x
2964 = x

x+1 = 2965

Answer: The other leg is 2964 m and the hypotenuse is 2965 m
User SkRoR
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