Question

The shortest side of an isosceles triangle is
`(3x-1)` meters long. The two longer sides are 5 meters longer than the shortest side. A regular octagon has sides that are
`(2x)` 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.

Answer 1

• triangle short side: 2 m
• triangle long side: 7 m
• octagon side: 2 m

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

__

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.