The length of the rectangular table is 5 inches longer than the width. The perimeter is at least 92 inches.
Which range shows the possible widths of the table?
A. w ≥ 10.50
B. w ≥ 15.50
C. w ≥ 20.50
D. w ≥ 25.50
Let's start by using algebra to find a formula for the perimeter of the table in terms of its width:
Perimeter = 2(length + width)
We know that the length is 5 inches longer than the width, so we can substitute (w + 5) for length:
Perimeter = 2((w + 5) + w)
Simplifying:
Perimeter = 2(2w + 5)
Perimeter = 4w + 10
Now we can use the given information that the perimeter is at least 92 inches to set up an inequality:
4w + 10 ≥ 92
Solving for w:
4w ≥ 82
w ≥ 20.5
So the width must be at least 20.5 inches. The only answer choice that includes this value is C, which is the correct answer.