Word problem

Question

Consider a square and regular hexagon. One side of the square is 26 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 Dd,

 

Let's begin by writing algebraic expressions to represent the side lengths of each figure:

    s = side length of hexagon

    s + 26 = side length of square

 

Next, let's write an equation to express the given fact that the perimeter of the square is equal to the perimeter of the hexagon and solve that equation for our unknowns, (s) and (s + 26):

    4(s + 26) = 6s

    4s + 104 = 6s

    6s - 4s = 104

    2s = 104

    s = 104/2

    s = 52 feet (side length of hexagon)

    s + 26 = 52 + 26

    s + 26 = 78 feet (side length of square)

 

Finally, let's verify our answers by plugging them back into our equation to check that both perimeters are equal:

    4(s + 26) = 6s

    4(78) = 6(52)

    312 = 312

 

Since both perimeters are shown to be the same length (312 feet), we are confident that our side lengths for the two figures are correct.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.

Answer 2

Let the side of the hexagon be h feet

 

Side of the square will be (h+26)feet

 

Perimeter of the hexagon will be 6 x h= 6h feet, (multiplied by 6 since all sides all equal)

 

Perimeter of the square will be 4(h +26) feet = 4h +104 feet

 

Same perimeter, therefore, 4h +104 = 6h

 

Subtracting 4h from both sides we are left with 

 

104 = 2h

 

Solve for h

 

h =52 feet 

 

h +26 =78 feet

 

Hexagon sides will be 52 feet each 

 

Square sides will be 78 feet each