The area of a triangle is 45 feet squared. If the base of the triangle is 4 less than half the height, what is the height and base of the trangle?
Let $\displaystyle x$ be the height,Originally Posted by leesh2009
then $\displaystyle \frac{1}{2}x-4$ is the base.
Since, area is 45 and you know that,
$\displaystyle \frac{1}{2}\times (\mbox{height})(\mbox{base})=\mbox{Area}$
Thus,
$\displaystyle \frac{1}{2}x\left(\frac{1}{2}x-4\right)=45$
Thus, open parantheses,
$\displaystyle \frac{1}{4}x^2-2x=45$
Now, multiply this by 4 to get,
$\displaystyle x^2-8x=180$
Thus,
$\displaystyle x^2-8x-180=0$
Thus,
$\displaystyle (x+10)(x-18)=0$
Thus,
$\displaystyle x=-10,18$ reject the negative.
Thus, $\displaystyle x=18$