Question

A 10-sided polygon has 4 sides each of

length p inches and 3 sides each of length
4p inches. The lengths of the other 3 sides
are 10 inches, 12 inches, and 4 inches. If
the perimeter of the polygon is 138 inches,
what is the length of the longest side of the
polygon?

E. 7 inches
F. 10 inches
G. 12 inches
H. 28 inches
​

Answer 1

Explanation:

Givens

4 sides = 4*p

3 sides = 3(4p) = 12p

Other sides

10

12

4

Total length = 138 inches

Equation

4p + 12p + 10 + 12 + 4 = 138

Solution

Collect like terms

16p + 26 = 138

Subtract 26 from both sides

16p + 26 - 26 = 138 - 26

16p = 112

Divide by 16

16p/16 = 112/16

p = 7

Longest Side (Answer)

7 * 4 = 28 inches

H