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

Answer:

36

Step-by-step explanation:

Answer 2

Answer:

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

Step-by-step 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

$P=6x$

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