A rectangular enclosure must have an area of at least 2400yd² . If 220yd of fencing is to be used, and the width cannot exceed the length, within what limits must the width of the enclosure lie? A) $0 \mathrm { yd } \leq \text { width } \leq 30 \mathrm { yd }$ B) $30 \mathrm { yd } \leq \text { width } \leq 80 \mathrm { yd }$ C) $55 \mathrm { yd } \leq \text { width } \leq 80 \mathrm { yd }$ D) $30 \mathrm { yd } \leq \text { width } \leq 55 \mathrm { yd }$

Question

Quizplus · Accepted Answer

The perimeter of the rectangle is 2(length + width) = 220 yards, so length + width = 110 yards. Since the area is length * width ≥ 2400 square yards and width cannot exceed length, the width must be at least 30 yards to ensure the area is at least 2400 square yards (since 30*80 = 2400 and 30+80=110). The maximum width is when width equals length, so width = 110/2 = 55 yards. Therefore, the width must lie between 30 and 55 yards.

A Rectangular Enclosure Must Have an Area of at Least 0yd≤ width ≤30yd0 \mathrm { yd } \leq \text { width } \leq 30 \mathrm { yd }0yd≤ width ≤30yd

A Rectangular Enclosure Must Have an Area of at Least $0 \mathrm { yd } \leq \text { width } \leq 30 \mathrm { yd }$