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The length of a rectangle is three more than twice the width. Determine the dimensions that will give a total area of .
Solution:
First we need to draw a picture to visualize the problem. Since the length is more that twice the width, we will have . So we have the following picture:
Now, since both parts of this question deal with the area of this rectangle, lets begin by generating a function for the area.
Since we have:
First, we want to know what dimensions make an area of . Thus, we can insert for into our function and solve for .
We have:
.........factor completely
solutions:
if ->
if ->
So, since represents the of a rectangle we must omit the negative value.Therefore, we have . Plugging that value into we get ->
Therefore, the dimensions that give the rectangle an area of are by .
