Question

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

Answer 1

let h be height and b the base. So we get that

$\begin{gathered} \frac{h\cdot b}{2}=27\rightarrow h\cdot b=54 \\ h=2b-3 \end{gathered}$

so we get that

$\begin{gathered} (2b-3)b=54 \\ 2b^2-3b-54=0 \\ (b-6)(2b+9)=0 \end{gathered}$

as b must be positive, we get that b=6, and therefore h=12-3=9