MATH SOLVE

2 months ago

Q:
# 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 + 30x + 216 D. f(x) = 3x2 + 216

Accepted Solution

A:

1) The
original swimming pool has a length of 18 feet, and 2) the new swimming pool will be 3x feet longer

=> new length = 18 + 3x

3) the original swimming poll has a width of 12 feet, the new swimming pool will be x feet wider

=> new width = 12 + x

New area = new length * new width

=> new area = (18 + 3x)(12 + x)

Apply distributive property: 18 * 12 + 18x + 12*3x + 3x*x

=> 216 + 54x + 3x^2

Β 4) arrange in decrasing order:

=> 3x^2 + 54x + 216

Answer: option B. f(x) = 3x^2 + 54x + 216

=> new length = 18 + 3x

3) the original swimming poll has a width of 12 feet, the new swimming pool will be x feet wider

=> new width = 12 + x

New area = new length * new width

=> new area = (18 + 3x)(12 + x)

Apply distributive property: 18 * 12 + 18x + 12*3x + 3x*x

=> 216 + 54x + 3x^2

Β 4) arrange in decrasing order:

=> 3x^2 + 54x + 216

Answer: option B. f(x) = 3x^2 + 54x + 216