Question

What is the height of the following triangle, if the area is 42 square units?

Answer 1

\(\large\color{blue}{ \rm 42\times 2=(2x+3)(4x+4)}\)
\(\large\color{blue}{ \rm 84=(2x+3)(4x+4)}\)
\(\large\color{blue}{ \rm 84=8x^2+20x+12}\)
\(\large\color{blue}{ \rm 21=2x^2+5x+3}\)
\(\large\color{blue}{ \rm 2x^2+5x-18=0}\)
\(\large\color{blue}{ \rm (x-2)(2x+9)=0}\)
\(\large\color{blue}{ \rm x=~2,~-9/2}\)

Answer 2

The height,

\(\large\color{blue}{ \rm 2x+3}\)
\(\large\color{blue}{ \rm 2(2)+3}\)
\(\large\color{blue}{ \rm 4+3}\)
\(\large\color{blue}{ \rm 7}\) is the answer.