Question

The height of a triangle is $2\mathrm{units}$ longer than its base. If the area is $12\mathrm{square}\mathrm{units}$, what is the length of the base?

Answer 1

Calculating the base of the triangle

Given,

The area of the triangle is $12\mathrm{square}\mathrm{units}$,

The height of a triangle is $2\mathrm{units}$ longer than its base.

Let the base of the triangle be $x\mathrm{units}$.

Then, the height of the triangle$=(2+x)units.$

Solving for the area of the triangle,

$$\begin{gathered} ar(∆)=\frac{1}{2}\times base\times height \\ \Rightarrow 12=\frac{1}{2}\left(x\right)(2+x) \\ \Rightarrow 24=x^2+2x \\ \Rightarrow 0=x^2+2x-24 \\ \Rightarrow (x+6)(x-4)=0 \\ \Rightarrow x=-6,4 \\ \Rightarrow x=4\left[\mathrm{side}\mathrm{cannot}\mathrm{be}\mathrm{negative}\right] \end{gathered}$$

Therefore, the length of the base of the triangle is $4\mathrm{units}$.