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lakkis [162]
3 years ago
13

The medium side of a right triangle is 7 more than the shortest side. The longest side is 7 less than 3 times the shorter side.

Find the length of the shortest side of the triangle.
Mathematics
1 answer:
sp2606 [1]3 years ago
6 0

Answer:

  8

Step-by-step explanation:

Let x represent the length of the shortest side. Then (x+7) is the length of the longer side, and (3x-7) is the length of the hypotenuse. The Pythagorean theorem gives the relation ...

  (3x -7)² = x² +(x +7)²

  9x² -42x +49 = x² +x² +14x +49

  7x² -56x = 0 . . . . . . . . . subtract the right side, simplify

  7x(x -8) = 0

Values of x that satisfy this equation are x=0 and x=8. We know x=0 is not a viable solution, so ...

the shortest side is 8 units long

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