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=(1)/(2)bh`

That is,

`\begin{gathered} 27=(1)/(2)* b*(2b-3)_{} \\ 54=2b^2-3b \\ 2b^2-3b-54=0 \end{gathered}`

Solving for b, we have,

`b=6`

therefore, height is,

`2*6-3=12-3=9`

Thu, base = 6, height = 9