SOLUTION: Suppose that the length of a rectangle is 3 inches longer than the width and that the perimeter of the rectangle is 78. A) Set up an equation involving only W, the width of the

Algebra ->  Equations -> SOLUTION: Suppose that the length of a rectangle is 3 inches longer than the width and that the perimeter of the rectangle is 78. A) Set up an equation involving only W, the width of the      Log On


   

Question 128616: Suppose that the length of a rectangle is 3 inches longer than the width and that the perimeter of the rectangle is 78.
A) Set up an equation involving only W, the width of the rectangle.
B) Solve this equation algebraically to find the length of the rectangle, find the width as well.
Length = Width =
Found 2 solutions by checkley71, solver91311:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
L=W+3
2L+2W=78
2(W+3)+2W=78
2W+6+2W=78
4W=78-6
4W=72
W=72/4
W=18 IS THE WIDTH.
L=18+3=21 IS THE LENGTH.
PROOF:
2*18+2*21=78
36+42=78
78=78

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


If the length measures 3 inches more than the width, and the width is w, then

the length is w + 3.  We know that the perimeter of a rectangle is given by

P%5Br%5D=2l+%2B+2w, so just substitute:





P%5Br%5D=2%28w%2B3%29%2B2w and we are given that P%5Br%5D=78





2%28w%2B3%29%2B2w=78





Distribute the 2 and remove the parentheses:

2w%2B6%2B2w=78





Collect like terms:

4w%2B6=78





Add -6 to both sides:

4w=72





And divide by 4:

w=18





The length is w+%2B+3=21





Check:

2 times 21 is 42, 2 times 18 is 36, and 42 plus 36 is 78.  Answer checks.