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 Please show your work
2(w+28) <= 120
w+28 <= 60
w <= 32
To find the inequality that represents the width of the pool, we can start by recalling that the perimeter of a rectangle is given by the formula: P = 2l + 2w, where P represents the perimeter, l represents the length, and w represents the width of the rectangle.
In this case, the length of the pool is given as 28 feet, and the perimeter must be no more than 120 feet. We can set up the inequality as follows:
2l + 2w ≤ 120
Substituting the given length value:
2(28) + 2w ≤ 120
Simplifying the equation:
56 + 2w ≤ 120
Next, we isolate the variable w by subtracting 56 from both sides of the inequality:
2w ≤ 120 - 56
2w ≤ 64
Lastly, we divide both sides of the inequality by 2 to solve for w:
w ≤ 64/2
w ≤ 32
Therefore, the inequality that represents the width of the pool is w ≤ 32. This means that the width of the pool must be less than or equal to 32 feet in order to satisfy the given perimeter condition.
Let's denote the width of the pool as 'w'.
To find the inequality representing the width of the pool, we need to consider the perimeter of the pool. The perimeter of a rectangle is given by the formula:
Perimeter = 2 × (length + width)
Since the length is given as 28 feet, the perimeter can be expressed as:
120 = 2 × (28 + w)
To solve for 'w', we can start by simplifying the equation:
120 = 56 + 2w
Now, isolate the variable 'w' by subtracting 56 from both sides of the equation:
120 - 56 = 56 - 56 + 2w
64 = 2w
Finally, divide both sides of the equation by 2 to solve for 'w':
w = 64/2
w = 32
Therefore, the width of the pool must be 32 feet or less to satisfy the given condition that the perimeter should not exceed 120 feet.