SOLUTION: The length of a square is 2x-5 and the length of a rectangle is 2x and the width measures x+2. For what value of x is the perimeter of the square the same as the perimeter of the r

Algebra ->  Rectangles -> SOLUTION: The length of a square is 2x-5 and the length of a rectangle is 2x and the width measures x+2. For what value of x is the perimeter of the square the same as the perimeter of the r      Log On


   

Question 731586: The length of a square is 2x-5 and the length of a rectangle is 2x and the width measures x+2. For what value of x is the perimeter of the square the same as the perimeter of the rectangle?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
if the length of a square is 2x-5, then P%5Bs%5D=4%282x-5%29

and if the length of a rectangle is L=2x and the width measures W=x%2B2
then P%5Br%5D=2%2A2x%2B2%28x%2B2%29...=>.. P%5Br%5D=4x%2B2%28x%2B2%29
if P%5Bs%5D=P%5Br%5D, then
4%282x-5%29=4x%2B2%28x%2B2%29.....solve for x
8x-20=4x%2B2x%2B4
8x-20=6x%2B4
8x-6x=20%2B4
2x=24
x=24%2F2
x=12


so, the length of a square is 2x-5..=>..2%2A12-5..=>..19
the length of a rectangle is L=2x ..=>..L=24
and the width measures W=x%2B2..=>..W=14

check if perimeters are same:
square
P%5Bs%5D=4%282x-5%29.....=>..P%5Bs%5D=4%282%2A12-5%29....=>..P%5Bs%5D=4%2A19..=>..P%5Bs%5D=76
rectangle
P%5Br%5D=4x%2B2%28x%2B2%29....=>...P%5Br%5D=4%2A12%2B2%2812%2B2%29...=>...P%5Br%5D=48%2B2%2814%29
..=>...P%5Br%5D=48%2B28.=>...P%5Br%5D=76
so, P%5Bs%5D=P%5Br%5D and highlight%28x=12%29 is your answer