What are the lengths of the sides of each figure?

Question

Consider a square and a regular hexagon (a six-sided figure with sides of equal length). One side of the square is 29 feet longer than a side of the hexagon, and the two figures have the same perimeter.

Answer 1

Let x = length of side of the hexagon, then x+29 = length of side of the square

 

Since the perimeters are the same:

 

6x = 4(x+29)

 

2x = 116

 

x = 58