Question 592700: what is the dimension of a rectangle whose perimeter is 34cm and the area is 66cm square?
Answer by mamiya(56)   (Show Source):
You can put this solution on YOUR website!
Let L be the length and, W the width
We know that the perimeter of a rectangle is 2L + 2W , and that its area is LW
So, we have : 2L + 2W = 34 --> L + W = 17
LW = 66 LW=66
At this point, there are many ways of solving it.
First, let's use the easiest way but sometimes the longest .
find all the two numbers whose product is 66,
we have: 1 and 66, 2 and 33, 3 and 22, 6 and 11
Now, look for the two combination in which the two numbers add up to 17
The only combination is 6 and 11 . So, the dimension are 6 and 11
The other way i am going to use is more complex.
first you need to pick one equation, write one variant in term of the other and plug in it in the other equation.
i chose the first equation, L+W=17 --> L = 17 - W
By plugging it the other equation, we get W( 17-W) = 66; Then , we solve for W
W(17-W) = 66 --> W^2 - 17W + 66 =0
Now we use the quadratic formula.
W=[17 + sqrt(-17^2 -4( 1)(66))]/ 2 and W=[17 - sqrt(-17^2 -4( 1)(66))]/
= (17 + 5)/2 =(17 - 5)/2
= 11 = 6
so, the dimensions are 11 and 6.
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