Adam is building a rectangular swimming pool. The perimeter of the pool must be no more than 120 feet. If the length of the pool is 28 feet, write and solve an inequality that represents what the width of the pool must be.
Please show your work
Let's assume that the width of the pool is W feet.
The perimeter of a rectangle can be calculated by adding the lengths of all its sides.
In this case, the perimeter of the pool is given as 120 feet, so we can write the inequality:
2(28 + W) ≤ 120
Simplifying the inequality:
56 + 2W ≤ 120
Subtracting 56 from both sides:
2W ≤ 64
Finally, dividing both sides by 2:
W ≤ 32
So the width of the pool must be no more than 32 feet.
Let's represent the width of the pool as "w".
Since the perimeter of a rectangle is the sum of all its sides, we can write the inequality to represent the perimeter:
2(length + width) ≤ 120
Substituting the given values, we have:
2(28 + w) ≤ 120
Simplifying further:
56 + 2w ≤ 120
To isolate "w" on one side of the inequality, we subtract 56 from both sides:
2w ≤ 120 - 56
2w ≤ 64
Finally, we divide both sides of the inequality by 2 to solve for "w":
w ≤ 64/2
w ≤ 32
Therefore, the width of the pool must be less than or equal to 32 feet.