SOLUTION: The widith of a rectangle is 3 cm less than the length. The area of a rectangle is 54cm^2. Find the widith and length.

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Question 700737: The widith of a rectangle is 3 cm less than the length. The area of a rectangle is 54cm^2. Find the widith and length.
Answer by Simnepi(216) About Me  (Show Source):
You can put this solution on YOUR website!
To solve problems like these you have to make an equation from the information given.
Let's call the length x.
Because the width is 3 less than the length, we can say that....
the width is (x-3).
We know that area = length x width. So now we can write
54 = x*(x-3).
Multiplying out the brackets gives
54 = x%5E2+-+3x
rearranging this gives
0+=+x%5E2+-+3x+-+54 OR x%5E2+-+3x+-+54+=+0
So we have a quadratic equation which will have 2 solutions.
To find what they are we have to find factors of -54. These are plus/minus 1 and 54, plus/minus 2 and 27, plus/minus 3 and 18, plus/minus 6 and 9.
Because there is -3x in the quadratic equation we are looking for factors which we can add or take to make to make -3.
Obviously, the factors we must choose are +6 and -9, these will multiply to make -54 and we can add them to make -3.
We will use those factors to factorise the equation x%5E2+-+3x+-+54+=+0
Thus we get
(x+6)(x-9) = 0
because one of these factors must equal 0 we can say that either
(x+6) = 0 OR (x-9) = 0
solving these linear equations gives
x = -6, OR x = 9
The first solution is nonsense as you can't have a negative measurement
so the length of the rectangle is 9 cm.
Hope that helps.