Final answer:
The rectangle has a width of 21 meters and a length of 23 meters, since its dimensions are consecutive odd integers and its perimeter is 88 meters.
Step-by-step explanation:
To find the length and width of a rectangle where the dimensions are consecutive odd integers and the perimeter is 88 meters, we first write the formula for the perimeter of a rectangle:
P = 2l + 2w
Since the length (l) and width (w) are consecutive odd integers, we can express the width as w and the length as w + 2 (since the next odd integer after an odd number w is w + 2). Substituting w and w + 2 into the formula gives us:
88 = 2(w + 2) + 2w
Expanding the equation, we have:
88 = 2w + 4 + 2w
Combining like terms:
88 = 4w + 4
Subtracting 4 from both sides:
84 = 4w
Divide both sides by 4:
w = 21
So the width is 21 meters. Then the length is w + 2 = 23 meters.
To summarize, the width of the rectangle is 21 meters, and the length is 23 meters.