SOLUTION: Please help me solve this. Ive just started learning and I do not understand. A rectangle has a perimeter of 130cm. If the length of the rectangle is 4 times its width, find the d

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Question 462234: Please help me solve this. Ive just started learning and I do not understand.
A rectangle has a perimeter of 130cm. If the length of the rectangle is 4 times its width, find the demensions of the rectangle.
Answer by JimboP1977(311) About Me  (Show Source):
You can put this solution on YOUR website!
The perimeter is the length around the border or outside of the rectangle.

The perimeter is made up of the length of the rectangle plus the other length plus the width plus the width.
Let P = perimeter.
Let L= length and W=width
So P+=+l%2Bl%2Bw%2Bw
Because we have two lots of l and two lots w we can write as
P+=%282%2Al%29%2B%282%2Aw%29

We also now that the length is 4 times the width or
l=4%2Aw

Now here is the clever bit. What we can do is subsitute 4*w from this equation into P+=%282%2Al%29%2B%282%2Aw%29
because know that l is the same as 4*w (THIS IS IMPORTANT TO SEE - DO YOU SEE THIS?)
So we get P+=%282%2A%284%2Aw%29%29%2B%282%2Aw%29
we can then multiply out the first bracket to give
P+=%288%2Aw%29%29%2B%282%2Aw%29
collect terms to give
P+=+10%2Aw

We know the perimeter is equal to 130cm so
130+=+10%2Aw
To find w we need to divide both sides by 10 to give
13+=+w

Can you work out the length?