The shorter leg of a right triangle is 8m shorter than the longer leg. The hypotenuse is 8m longer than the longer leg. Find the side lengths of the triangle.

  24 m, 32 m, 40 m

Step-by-step explanation:

The side lengths form an arithmetic sequence with common difference 8m. The only Pythagorean triple that is an arithmetic sequence is the one with ratios 3:4:5. So, the triangle side lengths must be ...

  3×8m = 24 m . . . . shorter leg

  4×8m = 32 m . . . . longer leg

  5×8m = 40 m . . . . hypotenuse

If you like, you can let x represent the length of the longer leg and use the Pythagorean theorem to write the relation ...

  (x)^2 +(x -8)^2 = (x +8)^2

  2x^2 -16x +64 = x^2 +16x +64

  x^2 -32x = 0 . . . . . . subtract the right side to get into standard form

  x(x -32) = 0 . . . . . . . factor

The only useful solution is x = 32, which makes one factor zero. This is the length of the longer side. The other lengths are 32±8 m.

The lengths of the sides are 24 m, 32 m, 40 m.

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