Question

Consider a square and a regular octagon (an 8

8
-sided figure with sides of equal length). One side of the square is 8
8
feet longer than a side of the octagon, and the two figures have the same perimeter. What are the lengths of the sides of each figure? (Round to two decimal places if necessary.)

Answer 1

• Sides are 16 ft for the square and 8 ft for the octagon.

--------------------------------------------------

Let the side of the square is x and side of the octagon is y.

Set equation for sides:

• x = y + 8

The perimeter of square is same as the perimeter of the octagon:

• 4x = 8y

Simplify and then substitute:

• 4x = 8y ⇒ x = 2y

• y + 8 = 2y
• y = 8

Find x:

• x = 8 + 8
• x = 16