Question

Sam needs to build a fence around his pool. The pool and the

sidewalk around it have a distance around of 200 feet, so the
perimeter of the fence needs to be at least 200 feet. The length of
the fence is five more than three times the width.
*<= is equivalent to s
*>= is equivalent to >
What should he make the length of his fence?
a) 65 feet
b) 40 feet
c) 35 feet
d) 60 feet

Answer 1

Sam should make the length of his fence at least 76.25 feet.

Step-by-step explanation:

The problem states that the perimeter of the fence needs to be at least 200 feet. Let's assume the width of the pool is 'w' feet. According to the problem, the length of the fence is five more than three times the width, so we can write it as '3w + 5' feet.

The perimeter of the fence is the sum of all the sides, which is 2 times the width plus 2 times the length: 2w + 2(3w + 5) = 2w + 6w + 10 = 8w + 10 feet.

Since the perimeter needs to be at least 200 feet, we can write the inequality: 8w + 10 >= 200. Solving for 'w', we get w >= 23.75. Therefore, Sam should make the length of his fence at least 3w + 5 = 3(23.75) + 5 = 71.25 + 5 = 76.25 feet.