Question

The height of a triangle is 3 yards less than twice the base. The area of the triangle is 27 square yards. Find the base and height of the triangle.

Answer 1

Given:

The height is, twice the base - 3, h = 2b - 3.

The area is, A = 27.

We have,

$A=\frac{1}{2}bh$

That is,

$\begin{gathered} 27=\frac{1}{2}\times b\times(2b-3)_{} \\ 54=2b^2-3b \\ 2b^2-3b-54=0 \end{gathered}$

Solving for b, we have,

$b=6$

therefore, height is,

$2\times6-3=12-3=9$

Thu, base = 6, height = 9