SOLUTION: The length of a rectangle is 4 times the width. The perimeter is 90 meters. What is the length and the width?

Question 903783: The length of a rectangle is 4 times the width. The perimeter is 90 meters. What is the length and the width?
Answer by tutoringisfun(17) (Show Source): You can put this solution on YOUR website!
Good evening student. I hope you find this solution helpful.
According, to the information given in the problem, we concur that L=4w. The formula for perimeter of a rectangle is P= 2L+2W. We can rewrite this as P=2(L+W). We need to solve for either L or W. Since I already know what L and P are I will plug that into the equation and solve for W, which gives me the following:
90=2(4w+w)now I use the distributive property and distribute the 2 to the equation inside the parenthesis like this: 90=2x4w+2w
when I simplify this it becomes 90=8w+2w
now I combine like terms to get the following:
90=10w
I want to get the W by itself, so I have to divide by 10, which gives me
9=w. I can rewrite it as w=9.
Now to find L I use the formula given in the problem L=4W,and substitute the 9 for the W. This gives me L=4(9). Solving this gives me L= 36.
L= 36
W=9
to check my answer, I can plug in both numbers into the formula for perimeter, that gives me 90=2(36+9). When I do the math I get 90=2(45). If I multiply this I get 90=90, which is a true statement so my answer is correct.

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