# The area of a particular triangle can be represented by x^2+3/2x-9/2. What are its base and height in terms of x?

Jan 6, 2017

The answer is $\left(2 x - 3\right)$ and $\left(x + 3\right)$

#### Explanation:

The area of a triangle is $= \frac{1}{2} \cdot b \cdot h$

so,

$\frac{1}{2} \cdot b \cdot h = {x}^{2} + \frac{3}{2} x - \frac{9}{2}$

$b \cdot h = 2 {x}^{2} + 3 x - 9$

$= \left(2 x - 3\right) \left(x + 3\right)$

Therefore,

$b = \left(2 x - 3\right)$

$h = \left(x + 3\right)$

or inversely