SOLUTION: please answer this: the width of a rectangular window frame is 12 inches less than its length. if you add 30 inches to both the length and the width, you double the perimeter. find

Algebra ->  Equations -> SOLUTION: please answer this: the width of a rectangular window frame is 12 inches less than its length. if you add 30 inches to both the length and the width, you double the perimeter. find      Log On


   

Question 331705: please answer this: the width of a rectangular window frame is 12 inches less than its length. if you add 30 inches to both the length and the width, you double the perimeter. find the length and the width of the original rectangle?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
the width of a rectangular window frame is 12 inches less than its length.
if you add 30 inches to both the length and the width, you double the perimeter.
find the length and the width of the original rectangle?
:
Find the original perimeter (P1)
P1 = 2L + 2W
"the width of a rectangular window frame is 12 inches less than its length."
P1 = 2L + 2(L-12)
P1 = 2L + 2L - 24
p1 = 4L - 24, the original perimeter
:
Find the doubled perimeter
"if you add 30 inches to both the length and the width,"
P2 = 2(L+30) + 2(W+30)
P2 = 2L + 60 + 2W + 60
P2 = 2L + 2W + 120
Replace W with (L-12)
P2 = 2L + 2(L-12) + 120
P2 = 2L + 2L - 24 + 120
P2 = 4L + 96,
:
It says the new perimeter = twice the old perimeter; P2 = 2(P1)
4L + 96 = 2(4L - 24)
4L + 96 = 8L - 48
96 + 48 = 8L - 4L
144 = 4L
L = 144%2F4
L = 36 in is the original length
then
36 - 12 = 24 in is the original width
:
:
You can check the solution by finding the old and the new perimeters