Question

a triangles area is given by the expression 3x² - x + 12. the height is 6x. the base of the triangle is the quotient of the area and 1/2 of the height. which expression represents the base of the triangle? o x/2 - 1/6 + 4/x o x - 1/3 + 4x o x/2 - 1/6 + 4x o x - 1/3 + 4/x

Explanation:

Step1: Find half of the height

Half of the height $h = 6x$ is $\frac{1}{2}\times6x=3x$.

Step2: Divide the area by half - height

The area $A = 3x^{2}-x + 12$. Divide $A$ by $3x$: $\frac{3x^{2}-x + 12}{3x}=\frac{3x^{2}}{3x}-\frac{x}{3x}+\frac{12}{3x}$.

Step3: Simplify the expression

$\frac{3x^{2}}{3x}=x$, $\frac{x}{3x}=\frac{1}{3}$, $\frac{12}{3x}=\frac{4}{x}$. So the base $b=x-\frac{1}{3}+\frac{4}{x}$.

Answer:

$x-\frac{1}{3}+\frac{4}{x}$