A square and a rectangle have the same perimeter. The square has a side length of 8x units. The rectangle has a length of (5x+8) units and a width of 14 units. What will the perimeter of both the rectangle and the square

Accepted Solution

Answer:The perimeter of both figures is equal to [tex]64\ units[/tex]Step-by-step explanation:step 1we know thatThe perimeter of a square is equal to[tex]P=4b[/tex]whereb is the side length of the squarewe have[tex]b=8x\ units[/tex]substitute[tex]P=4(8x)=32x\ units[/tex]step 2we know thatThe perimeter of a rectangle is equal to[tex]P=2(L+W)[/tex]we have[tex]L=(5x+8)\ units[/tex][tex]W=(14)\ units[/tex]substitute[tex]P=2(5x+8+14)=10x+44\ units[/tex]step 3Equate both perimeters and solve for x[tex]10x+44=32x[/tex][tex]32x-10x=44[/tex][tex]22x=44[/tex][tex]x=2\ units[/tex]step 4Find the perimeter of bothsquare[tex]P=32x=32(2)=64\ units[/tex]rectangle[tex]P=10x+44=10(2)+44=64\ units[/tex]