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patriot [66]
3 years ago
12

The length of the longer leg of a right triangle is 6 inches more than twice the length of the shorter leg. The length of the hy

potenuse is 9 inches more than twice the length of the shorter leg. Find the side lengths of the triangle.​
Mathematics
1 answer:
Studentka2010 [4]3 years ago
6 0

9514 1404 393

Answer:

  15 in, 36 in, 39 in

Step-by-step explanation:

The Pythagorean theorem tells us that for short side x, the relation is ...

  (2x +9)² = (2x +6)² +x²

  4x² +36x +81 = 4x² +24x +36 +x²

  x² -12x -45 = 0 . . . . . subtract the left-side expression

  (x -15)(x +3) = 0 . . . . factor

  x = 15 . . . . . . . . . . . the positive value of x that makes a factor zero

The side lengths of the triangle are 15 inches, 36 inches, and 39 inches.

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