Question

5
select the correct answer.
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. $f(x) = 15x^2 + 420x + 2400$
b. $f(x) = 15x^2 + 2400$
c. $f(x) = 15x^2$
d. $f(x) = 15x^2 + 380x + 2400$

Explanation:

Step1: Find new width and length

New width: \( 40 + 3x \); New length: \( 60 + 5x \)

Step2: Calculate area (width×length)

\( (40 + 3x)(60 + 5x) = 40×60 + 40×5x + 3x×60 + 3x×5x \)

Step3: Simplify the expression

\( 2400 + 200x + 180x + 15x^2 = 15x^2 + 420x + 2400 \)

Answer:

A. \( f(x) = 15x^2 + 420x + 2400 \)