Question

The height of a triangle is three more than two times the base. The area of the triangle is 45 square feet. What are the dimensions of the triangle? solve by factoring

Answer 1

The height of a triangle is three more than two times the base, can be translated algebraically as

`h=3+2b`

If the area of the triangle is 45 square feet, then we can have the equation

`\begin{gathered} h=3+2b \\ 2b=h-3 \\ b=(h-3)/(2) \\ \; \\ A=(1)/(2)bh \\ 45=(1)/(2)((h-3)/(2))(h) \\ 45\cdot4=((h-3)h)/(4)\cdot4 \\ 180=(h-3)(h) \\ h^2-3h-180=0 \\ (h-15)(h+12)=0 \\ \; \\ h-15=0 \\ h=15 \\ \; \\ h+12=0 \\ h=-12 \end{gathered}`

Disregarding the negative values for h, we use h = 15. And then use this to solve for the base

`\begin{gathered} h=3+2b \\ 15=3+2b \\ 15-3=2b \\ 2b=12 \\ b=6 \end{gathered}`

The dimensions therefore of the triangle is height of 15 feet, and a base of 6 feet.