SOLUTION: A banner is in the shape of a right triangle of area 63in sq. The height of the banner is 4in less than twice the width of the banner. find the height and the width of the banner.

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Question 412159: A banner is in the shape of a right triangle of area 63in sq. The height of the banner is 4in less than twice the width of the banner. find the height and the width of the banner.
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
The formula for area of a triangle is:

Let x = width of the banner. The height, which is "4in less than twice the width" would then be: 2x-4.

Substituting these expressions and the given area into the area formula we get:

To solve this we start by simplifying:

Since this is a quadratic equation we want one side to be zero. Subtracting 63 from each side we get:

Now we factor (or use the Quadratic Formula). This factors easily:
0 = (x+7)(x-9)
From the Zero Product Property we know that one of these factors must be zero. So:
x+7 = 0 or x-9 = 0
Solving these we get:
x = -7 or x = 9
Since x is the width of the banner and banners do not have negative widths, we will reject the negative solution. So x = 9. And the height, 2x-4, would be 2(9)-4 or 14.