Question

If two similar polygons have perimeters of 36 and 21 inches.

If the length of the side of the larger rectangle is 14 inches, then what is the product of the lengths of the polygons?

Answer 1

91

Explanation:

Two similar polygons, means a similarity would exist in both polygons

• Perimeter of a rectangle = 2(l +w)
• Perimeter of the larger rectangle = 36 (because it's the largest figure)
• equation becomes 36 = 2(L + W)
• since L = 14, it becomes = 36 = 2(14 +W)
• 36 = 28 + 2W
• 2W = 36 - 28 = 2w = 8

• w = 4.

Now we assume that since the rectangles are similar, they would have similar dimensions, in this case Width. so with this, we find length of smaller rectangle.

• 21 = 2(L + 4) = 21 = 2L + 8

• 2L = 21 - 8 = 2L = 13

• L = 13/2 = 6.5.

lastly the product of the length of both polygons = 14 * 6.5 = 91.

Their Products length is 91