Question

A regular hexagon and a rectangle have the same perimeter, P. A side of the hexagon is 4 less than the length, l, of the rectangle. The width of the rectangle, w, is 2 less than the length of the rectangle. What is the perimeter of the hexagon?

Answer 1

36

Explanation:

Answer 2

The perimeter of the hexagon is equal to
`36\ units`

Explanation:

Let

x-------> the length side of the hexagon

L-----> the length of the rectangle

W-----> the width of the rectangle

we know that

The perimeter of the hexagon is equal to

`P=6x`

The perimeter of the rectangle is equal to

`P=2L+2W`

so

`6x=2L+2W`

`3x=L+W` -------> equation A

`x=L-4` -------> equation B

`W=L-2` -------> equation C

Substitute equation B and equation C in equation A

`3[L-4]=L+[L-2]`

Solve for L

`3L-12=2L-2`

`3L-2L=12-2`

`L=10\ units`

Find the value of x

`x=L-4`

`x=10-4=6\ units`

Find the perimeter of hexagon

`P=6x`

`P=6(6)=36\ units`