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A triangle has the following side lengths: x - 2, x, and 3x + 1. Another triangle has the following side lengths: 2x - 5, x + 4, 6x - 7. If the perimeters of the two triangles are equal, what is x?

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Given

  • triangle 1 has side lengths (x-2), x, (3x+1)
  • triangle 2 has side lengths (2x-5), (x+4), (6x-7)
  • the two triangles have the same perimeter

Find

  • x

Solution

The perimeter is the sum of the lengths of the sides. The given information means ...

... (x-2) + x + (3x+1) = (2x-5) + (x+4) + (6x-7)

... 5x -1 = 9x -8 . . . . . simplify

... 0 = 4x -7 . . . . . . . . subtract the left side

... 0 = x -7/4 . . . . . . . .divide by the coefficient of x

... x = 7/4

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