Question

The length of each side of a square is 6 feet more than the length of a side of a regular Octagon. The perimeter of the square is equal to the octagon. Find the length of the square and the length of a side of the octagon.
Please show work, I will give brainliest.

Answer 1

9514 1404 393

Answer:

• square: 12 ft sides
• octagon: 6 ft sides

Step-by-step explanation:

This problem can be worked in your head.

If the perimeters of the square and regular octagon are the same, the side length of the 4-sided square must be the same as the length of 2 sides of the 8-sided octagon. Since the side of the square is 6 ft more than the side of the octagon, each side of the octagon must be 6 ft, and each side of the square must be 12 ft.

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We can let s represent the side length of the octagon. Then we have ...

  8s = perimeter of octagon

  4(s +6) = perimeter of square

These are equal, so ...

  4(s +6) = 8s

  s +6 = 2s . . . . . . divide by 4

  6 = s . . . . . . . . . . subtract s

The octagon has 6-ft sides; the square has 12-ft sides.