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 Ratio And Perimeter of a Rectangle
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firststopfirststop
Junior Member

United Kingdom
3 Posts

Posted - 11/19/2007 :  12:34:03  Show Profile  Reply with Quote
Hi there,

Can someone please help me on the question below?

Q1 - The length to width ratio of a rectangle is 1.5. If the perimeter is 100mm, find its length and width?

Many Thanks
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tkhunny
Advanced Member

USA
1001 Posts

Posted - 11/19/2007 :  14:22:20  Show Profile  Reply with Quote
What does "Ratio" mean?

1 and 5 make what ratio? Either 1/5 = 5/1, right?

So, length to width have a ratio of 1.5, this means Length/Width = 1.5. This should make sense, as normally, the length would be greater than the width.

What does "Perimiter" mean? Around a rectangle that it the width in the front and another width in the back. This is in addition to the length on one side and another length on the other side.

So Perimeter = 2*Width + 2*Length = 100 mm

Okay, we have these:

2*Width + 2*Length = 100 mm
Length/Width = 1.5

Now what?

You must THINK THROUGH problems of any nature. They will not jump up and bite you. Reach out. Grab them. Examine them upside down and inside out. Bring in all the stuff you know. I know you know it. There is a reason why you studied rations and rectangles. You need that information right now. Use it!
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the_hill1962
Advanced Member

USA
1468 Posts

Posted - 11/26/2007 :  07:45:26  Show Profile  Reply with Quote
Dealing with ratios can be confusing to a beginning math student (or anyone that gets confused with math in general).
As tkhunny pointed out, a ratio is a fraction. In your problem, the fraction (in simplest terms using integers only) is 3/2 since 3/2=1.5
This ratio can also be written as "3:2"
However, as with most math problems, there are different ways to tackle or think about solutions.
Put quite simply, a ratio of "1.5" can be taken literally as meaning that one item is 1.5 times larger than the other item. The two items in your problem are Length and Width.
So, if you assume that the Length is the greater quantity (it really doesn't matter in this problem since it isn't specified----of course different math problems may have to be specified----just another minor irritation), you can write L=1.5W since length is 1.5 times larger than width.
Now, you can work with L=1.5W
Since perimeter (as tkhunny pointed out) is 2W+2L, you write
2W+2L=100. If you have 2 variables, you need two equations. Well, the other equation is L=1.5W
At this point, again, there are different methods to takle or think about proceding.
Have you have any experience solving systems of equations?
This system
L=1.5W
2W+2L=100
is most easily solved by substitution (put "1.5W" in for the L since we know L=1.5W
So, 2W+2L=100 becomes 2W+2(1.5W)=100.
You should have the skill to solve this problem now.
If you would like to see other methods of solving this problem, let us know.
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