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Find the dimensions of the rectangle

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In this problem we have the length (l) and the area (A) of a triangle. The length is 4 more than the width. we can have the width be represented by w. Therefore, if the length of the triangle is 4 more than the width, the length would be: w + 4.
 
The equation for finding the area of a rectangle is: A = lw
 
If if I fill out the equation with our filler values, we get: 96cm2 = (w+4)(w). Then you solve - 
 
96cm2 = (w+4)(w)
96 = w2 + 4w
0 = w2 + 4w - 96
 
Oh hey, quadratic equation! First we need to separate it into two parts.
0 = (w +   )(w -   ) Cool. Now we need two numbers whose product = 96, and whose difference = 4.
0 = (w + 12)(w - 8) Awesome. Now set each side equal to 0 and solve. Why? Because anything times 0 equals 0. Therefore, the equation will be true as long as one of those two parts is equal to 0.
 
w + 12 = 0
w = -12
 
w - 8 = 0
w = 8
 
w = -12 ; w = 8. Only one of these answers is possible for a measurements. You can't have negative length measurements because then you're traveling into other dimensions. And if you are, please take picture, that is groundbreaking science.
 
So there's the width! w = 8. So what's the length again? Oh right 4 more than the width.
 
l = 12 and w = 8.

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