Question

Jason is planning to increase the size of the swimming pool in his backyard. The original swimming pool has a length of 18 feet and a width of 12 feet. The new swimming pool will be 3x feet longer and x feet wider than the original swimming pool. Which of the following functions will give the surface area of the new swimming pool in square feet?
A. f(x) = 3x2 + 66x + 216
B. f(x) = 3x2 + 54x + 216
C. f(x) = 3x2 + 216
D. f(x) = 3x2 + 30x + 216

Answer 1

The given length is 18 feet. The new pool will be 3x feet longer, this means that:
new length = 18 + 3x feet ............> equation I

The given width is 12 feet. The new pool will be x feet wider, this means that:
new width = 12 + x feet ...........> equation II

Now, the area of the rectangle = length * width
This means that to get the area, we will have to multiply equation I and II as follows:
area = (18+3x)(12+x)

Use the distributive property as follows:
area = (18+3x)(12+x)
area = 216 + 18x +36x + 3x^2
area = 3x^2 + 54x + 216

Comparing the calculated area with the given choices, we will find that the correct choice is:
B. f(x) = 3x2 + 54x + 216

Answer 2

Well, you'd first add the length (18 feet) to the extension (3x).
New length is 18 + 3x.
Then you'd add the width (12 feet) to the other extension (x).
New width is 12 + x.
Now, remember the equation Area = length x width? We're gonna have to multiply these terms together... sigh.
Here we go!
Area = (18 + 3x)(12 + x) You could use FOIL, but I'll factor for now.
18(12+x)+3x(12+x)
(216 + 18x) + (36x + 3x^2)
3x^2 + 54x +216
$3 x^{2} +54x+216$
Oh look! That's B. B is the answer.