Question

Consider a square and a regular hexagon (a six-sided figure with sides of equal length). One side of the square is 19 feet longer than a side of the hexagon, and the two figures have the same perimeter. What are the lengths of the sides of each figure?​

Answer 1

Hi there,

Make the side of the hexagon = x

Side of square = x + 12

Both figures have the same perimeters.

4(x + 14) = 6x

4x + 56 = 6x

Collect like terms:

6x - 4x = 56

2x = 56

x = 28

Length of hexagon side = 28 feet

Length of square side = 42 feet

Hope this helps :-)

Answer 2

square side = 57

hexagon side = 38

Explanation:

x = side length of square

y = side length of hexagon

x = y + 19

4x = 6y

substitute for x:

4(y + 19) = 6y

4y + 76 = 6y

subtract 4y from each side of the equation:

2y = 76

divide both sides by 2:

y = 38

x = 57