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?
Accepted Solution
A:
Answer:The perimeter of the hexagon is equal to [tex]36\ units[/tex]Step-by-step explanation:Letx-------> the length side of the hexagonL-----> the length of the rectangleW-----> the width of the rectanglewe know thatThe perimeter of the hexagon is equal to[tex]P=6x[/tex]The perimeter of the rectangle is equal to[tex]P=2L+2W[/tex]so[tex]6x=2L+2W[/tex] [tex]3x=L+W[/tex] -------> equation A[tex]x=L-4[/tex] -------> equation B[tex]W=L-2[/tex] -------> equation CSubstitute equation B and equation C in equation A[tex]3[L-4]=L+[L-2][/tex]Solve for L[tex]3L-12=2L-2[/tex][tex]3L-2L=12-2[/tex][tex]L=10\ units[/tex]Find the value of x[tex]x=L-4[/tex][tex]x=10-4=6\ units[/tex]Find the perimeter of hexagon[tex]P=6x[/tex][tex]P=6(6)=36\ units[/tex]