The shortest side of an isosceles triangle is meters long. the two longer sides are 5 meters longer than the shortest side. a regular octagon has sides that are meters long. the two shapes have the same perimeter. find the lengths of each side of the two shapes.

the length of the shortest side of the isosceles triangle is m.
the length of each of the longer sides of the isosceles triangle is m.
the length of each side of the octagon is m.

Step-by-step explanation:

The perimeter of the triangle is the sum of the lengths of its sides:

  (3x -1) + 2(3x -1 +5) = 9x +7

The perimeter of the octagon is the sum of the lengths of its sides:

  8(2x) = 16x

These two perimeters are reportedly the same, so we have ...

  9x +7 = 16x

  7 = 7x

  x = 1

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The length of the shortest triangle side is 3x-1 = 3·1 -1 = 2 meters.

The length of each of the longer triangle sides is 2+5 = 7 meters.

The length of each octagon side is 2·1 = 2 meters.