Question

A square has a side length of x + 3. A regular octagon has a side length of 3x. If the polygons have the same perimeter, determine the value of x.

Answer 1

x = ⅗ = 0.6

Explanation:

A square has four equal sides.

If a square has a side length of
`x + 3`, therefore,

Perimeter of the square =
`4(x + 3)`

`= 4x + 12`.

Also, a regular octagon has 8 equal sides.

If it has a side length of 3x, therefore:

Perimeter of the octagon =
`8(3x)`

=
`24x`

Given that the Perimeter of the rectangle and the octagon are the same, to find the value of x, set each perimeter equal to the other.

Thus:

`24x = 4x + 12`

Subtract 4x from each side

`24x - 4x = 12`

`20x = 12`

Divide both sides by 20

x = 12/20 = ⅗ = 0.6.