Question

the dimensions of a rectangle are represented by the functions shown. which function represents the area of the rectangle? (f(x)=2x - 9) (g(x)=3x - 4) (6x^{2}-8x + 36) (6x^{2}-27x + 36) (6x^{2}-35x + 36) (6x^{2}+35x + 36)

Explanation:

Step1: Recall area formula

The area $A$ of a rectangle is $A = l\times w$, where $l$ and $w$ are the length and width. Here, if $l = 2x - 9$ and $w=3x - 4$, then $A=(2x - 9)(3x - 4)$.

Step2: Expand the product

Using the FOIL method:
\[

$$\begin{align*} (2x-9)(3x - 4)&=2x\times3x+2x\times(- 4)+(-9)\times3x+(-9)\times(-4)\\ &=6x^{2}-8x-27x + 36\\ &=6x^{2}-35x + 36 \end{align*}$$

\]

Answer:

$6x^{2}-35x + 36$