Question 412159
The formula for area of a triangle is:
{{{A = (1/2)b*h}}}
Let x = width of the banner. The height, which is "4in less than twice the width" would then be: 2x-4.<br>
Substituting these expressions and the given area into the area formula we get:
{{{63 = (1/2)(x)(2x-4)}}}
To solve this we start by simplifying:
{{{63 = x^2 -2x}}}
Since this is a quadratic equation we want one side to be zero. Subtracting 63 from each side we get:
{{{0 = x^2 -2x -63}}}
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.