Question

Mario wants to put a rectangular fence around the pool in his backyard. Since one side is adjacent to the house, he will only need to fence three sides. There is one long side parallel to the house, and two shorter sides. He needs 130 feet of fencing to enclose the pool. The length of the long side is 10 feet less than twice the width. Find the length and width of the pool area to be enclosed.

Answer 1

Answer:

The length and width of the pool area is:

• Length = 60 feet.
• Width = 35 feet.

Step-by-step explanation:

Since the 130-foot fence should enclose only three parts of the pool (two wide and one long), equations are performed to express the information provided.

First an equation that says the total feet in the fence:

1. X + 2Y = 130 (where X is the length and Y is the width)
2. X = 2Y-10 (since the length is 10 feet less than twice the width)

With these equations, we proceed to replace the second equation in the first one and solve for Y:

• X + 2Y = 130
• 2Y -10 + 2Y = 130
• 4Y - 10 = 130
• 4Y = 130 + 10
• Y = 140/4
• Y = 35 feet

Since we already know that the width corresponds to 35 feet, we use the second equation to find the value of X:

• X = 2Y-10
• X = 2 (35) -10
• X = 70 - 10
• X = 60

With which it is identified that the length is 60 feet.