Question

the area of a rectangle is found by multiplying the base times the height. a rectangle with an area represented by 12x² + 6x - 8 has a height of 4x. what is the base of the rectangle? o 3x + 3/2 - 2/x o 3x² + 3/2 - 2/x o 3x + 3x/2 - 2/x o 3x + 3/2 - 1/2x

Explanation:

Step1: Recall area formula

The area formula of a rectangle is $A = b\times h$, where $A$ is the area, $b$ is the base and $h$ is the height. We need to solve for $b$, so $b=\frac{A}{h}$.

Step2: Substitute given values

Given $A = 12x^{2}+6x - 8$ and $h = 4x$. Then $b=\frac{12x^{2}+6x - 8}{4x}$.

Step3: Divide each term

Divide each term in the numerator by $4x$:

• $\frac{12x^{2}}{4x}=3x$.
• $\frac{6x}{4x}=\frac{3}{2}$.
• $\frac{- 8}{4x}=-\frac{2}{x}$.

So $b = 3x+\frac{3}{2}-\frac{2}{x}$.

Answer:

A. $3x+\frac{3}{2}-\frac{2}{x}$