Question 229854
The side of a square has length s. The length of a rectangle is 4 meters more than the side of the square and the width of the rectangle is 2 meters less than the side of the square. The perimeter of the rectangle is 24 meters less than twice the perimeter of the square. Find the dimensions of each figure.
:
s = side of the square
then
(s+4) = length of the rectangle
and
(s-2) = width of the rectangle
:
Given: "The perimeter of the rectangle (Pr) is 24 meters less than twice the perimeter of the square (Ps)"
Pr = 2Ps - 24
:
Pr = 2(s+4) + 2(s-2); (perimeter of the rectangle)
Pr = 2s + 8 + 2s - 4
Pr = 4s + 4
and
Ps = 4s; (perimeter of the square)
therefore
4s + 4 = 2(4s) - 24
4s + 4 = 8s
4 + 24 = 8s - 4s
28 = 4s
s = {{{28/4}}}
s = 7 meters is the side of the square
then
7+4 = 11 m is the length of the rectangle
and
7-2 = 5 m is the width of the rectangle
:
Sumarize: side of square = 7m, Rectangle 11 by 5 m
:
Check this in the statement:
"The perimeter of the rectangle (Pr) is 24 meters less than twice the perimeter of the square (Ps)"
2(11) + 2(5) = 2(4(7)) - 24 
22 + 10 = 2(28) - 24
32 = 56 - 24
;
Were these steps clear to you?