SOLUTION: 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 squar

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. Can you show me how to step up the equation correctly?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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 =
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?
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