SOLUTION: "The square and rectangle shown below have the same perimeter. *square* (2x+2)cm *Rectangle* (x+3)cm Show that the length

Algebra ->  Rectangles -> SOLUTION: "The square and rectangle shown below have the same perimeter. *square* (2x+2)cm *Rectangle* (x+3)cm Show that the length      Log On


   

Question 920434: "The square and rectangle shown below have the same perimeter.
*square* (2x+2)cm *Rectangle* (x+3)cm

Show that the length of the rectangle is (3x+1)cm
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
given:
*square* L%5Bs%5D=%282x%2B2%29cm+ => P%5Bs%5D=4%282x%2B2%29cm+
*Rectangle* W%5Br%5D=%28x%2B1%29cm+ => P%5Br%5D=2%28x%2B1%29cm%2B2%28x%2B3%29cm+
P%5Bs%5D=P%5Br%5D
Show that the length of the rectangle is L=%283x%2B1%29cm
since P%5Bs%5D=P%5Br%5D we have
if W%5Br%5D=%28x%2B1%29cm+ and L=%283x%2B1%29cm=>P%5Br%5D=+2%283x%2B1%29cm%2B2%28x%2B3%29cm+
and it is equal to P%5Bs%5D=4%282x%2B2%29cm+
so,
4%282x%2B2%29cm=+2highlight%28%283x%2B1%29%29cm%2B2%28x%2B3%29cm ...solve it and see if left side is equal to right side:

8x%2B8cm=+6x%2B2cm%2B2x%2B6cm

8x%2B8cm=8x%2B8cm ...highlight%28true%29, so the length of the rectangle is highlight%28%283x%2B1%29%29cm