SOLUTION: The ratio between the perimeter and the width of a rectangle is 14 : 3. If the area of the rectangle is 108 sq. cm, what is the length of the rectangle?

Algebra ->  Rectangles -> SOLUTION: The ratio between the perimeter and the width of a rectangle is 14 : 3. If the area of the rectangle is 108 sq. cm, what is the length of the rectangle?       Log On


   

Question 905445: The ratio between the perimeter and the width of a rectangle is 14 : 3. If the area of the rectangle is 108 sq. cm, what is the length of the rectangle?
Found 2 solutions by JoelSchwartz, Math_Boss:
Answer by JoelSchwartz(130) About Me  (Show Source):
You can put this solution on YOUR website!
A=108
108=Lw
w=108/L
p/w=14/3
p=2L+2w
(2L+2w)/w=14/3
2L+2w=14/3w
2L+2(108/L)=14/3(108/L)
2L+216/L=504/L
2L^2=504-216
2L^2=288
L^2=144
L=12
w=108/12
w=9
p=2*12+2*9
p=24+18
p=42
p/w=14/3
42/9=14/3
(42/9)/3=14/3
(42/3)/(9/3)=14/3
14/3=14/3

Answer by Math_Boss(45) About Me  (Show Source):
You can put this solution on YOUR website!
p=2%28l%2Bw%29
A=l%2Aw
108=lw
w=108%2Fl
p%2Fw=14%2F3
Substitute p=2(l+w)
2%28l%2Bw%29%2Fw=14%2F3
3%2A2%28l%2Bw%29=14w
6%28l%2Bw%29=14w
6l%2B6w=14w
6l=14w-6w
6l=8w
Substitute w=(108/l)
6l=8%28108%2Fl%29
6l=864%2Fl
Multiply by l
6l%5E2=864
Divide by 6
l%5E2=144
l=12
l=-12 (reject)
Ans:l=12 cm