SOLUTION: A rectangle has a length that is five times longer than its width. If the perimeter of the rectangle is 12 inches, what is the width? I got the equation 5w+w=12 and with that

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A rectangle has a length that is five times longer than its width. If the perimeter of the rectangle is 12 inches, what is the width? I got the equation 5w+w=12 and with that      Log On


   



Question 954398: A rectangle has a length that is five times longer than its width. If the perimeter of the rectangle is 12 inches, what is the width?

I got the equation 5w+w=12 and with that i added 5w+w and got 6w=12... After that i divided 6w and got 2... That was the wrong answer... My teacher said it was one and didnt explain how to get that answer... I am just confused... If you could help me it would be extremely appreciated..

Found 3 solutions by Alan3354, macston, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangle has a length that is five times longer than its width. If the perimeter of the rectangle is 12 inches, what is the width?
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I got the equation 5w+w=12 and with that i added 5w+w and got 6w=12... After that i divided 6w and got 2... That was the wrong answer... My teacher said it was one and didnt explain how to get that answer... I am just confused... If you could help me it would be extremely appreciated..
Perimeter = 2W + 2L = 12
W + L = 6, not 12 --> your calculations would be 1.
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But, 5 times longer is not 5 times as long, it's 6 times.
W + 6W = 6
W = 6/7 inches
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If 5 times longer = 5 times as long, what is 1 time longer? --> a 100% increase = 2 times as long.

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
W=width; L=length=5W: P=perimeter=2(L+W)=12 inches
P=2(L+W)
12 in=2(L+W)
6 in=L+W
6 in=5W+W
6 in=6W
1 in=W ANSWER: The width is 1 inch.
CHECK
L=5w=5 in
P=2(L+W)
12 in=2(5 in+1 in)
12 in=2(6 in)
12 in=12 in

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
a rectangle with a length L and a width W
given that a rectangle has a length L that is five times longer than its width W
=> L=5W
given that the perimeter of the rectangle is P=12in, and you know that P=2L%2B2W

so,2L%2B2W=12in
since given that L=5W,substitute it in 2L%2B2W=12in
2%2A5W%2B2W=12in...........solve for W
10W%2B2W=12in
12W=12in
W=12in%2F12
highlight%28W=1in%29

so,the width is highlight%281in%29
then the length is highlight%285in%29

check perimeter:
P=2%2A5in%2B2%2A1in
P=10in%2B2in
P=12in