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He length of one leg of a right triangle is 10 ft. The length of the hypotenuse is 2 feet longer than the other leg.Find the length of the hypotenuse and the other leg.

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sqdancefan

Answer:

  • hypotenuse: 26 ft
  • other leg: 24 ft

Step-by-step explanation:

This is a 5-12-13 right triangle scaled by a factor of 2 feet. (It helps to know some Pythagorean triples commonly used in algebra problems.)

The two longer sides are 24 feet and 26 feet.

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You can let x represent the length of the hypotenuse. Then you have ...

  x² = (x -2)² + 10²

  0 = -4x +104 . . . . . subtract x² and simplify

  x = 26 . . . . . . . . . . divide by 4, add x

The hypotenuse is 26; the other leg is 24.

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