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? :confused:

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- Mar 30th 2006, 11:17 AMleesh2009[SOLVED] algebra word problems
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? :confused:

- Mar 30th 2006, 01:20 PMThePerfectHackerQuote:

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, $\displaystyle x=18$