Question

joe wants to enlarge the rectangular pumpkin patch located on his farm. the pumpkin patch is currently 40 meters wide and 60 meters long. the new pumpkin patch will be 3x meters wider and 5x meters longer than that of the original pumpkin patch.
which of the following functions will give the area of the new pumpkin patch in square meters?
a. $f(x) = 15x^2$
b. $f(x) = 15x^2 + 2,400$
c. $f(x) = 15x^2 + 380x + 2,400$
d. $f(x) = 15x^2 + 420x + 2,400$

Explanation:

Step1: Define new dimensions

Original width: $40$ m, new width: $40 + 3x$
Original length: $60$ m, new length: $60 + 5x$

Step2: Apply area formula

Area $f(x) = (\text{new width}) \times (\text{new length}) = (40+3x)(60+5x)$

Step3: Expand the product

$$\begin{align*} f(x)&=40\times60 + 40\times5x + 3x\times60 + 3x\times5x\\ &=2400 + 200x + 180x + 15x^2\\ &=15x^2 + 380x + 2400 \end{align*}$$

Answer:

C. $f(x) = 15x^2 + 380x + 2,400$