# The area of a triangle is 24cm² [squared]. The base is 8cm longer than the height. Use this information to set up a quadratic equation. Solve the equation to find the length of the base?

Mar 10, 2018

Let the length of the base is $x$,so height will be $x - 8$

so,area of the triangle is $\frac{1}{2} x \left(x - 8\right) = 24$

or, ${x}^{2} - 8 x - 48 = 0$

or, ${x}^{2} - 12 x + 4 x - 48 = 0$

or, $x \left(x - 12\right) + 4 \left(x - 12\right) = 0$

or, $\left(x - 12\right) \left(x + 4\right) = 0$

so,either $x = 12$ or $x = - 4$ but length of triangle can't be negative,so here length of the base is $12$ cm

Mar 10, 2018

$12 c m$

#### Explanation:

The area of a triangle is $\frac{\text{base " xx " height}}{2}$

Let the height be $x$ then if the base is 8 longer, then the base is $x + 8$

$\implies \frac{x \times \left(x + 8\right)}{2} = \text{ area }$

$\implies \frac{x \left(x + 8\right)}{2} = 24$

$\implies x \left(x + 8\right) = 48$

Expanding and simplifying...

$\implies {x}^{2} + 8 x = 48$

$\implies {x}^{2} + 8 x - 48 = 0$

$\implies \left(x - 4\right) \left(x + 12\right) = 0$

$\implies x = 4 \text{ and } x = - 12$

We know $x = - 12$ can't be a solution as length can't be negative

Hence $x = 4$

We know the base is $x + 8$

$\implies 4 + 8 = 12$