A company needs to build a warehouse with perimeter $700 \mathrm { ft }$ . Find the dimensions to give maximum floor space.
A) $175 \mathrm { ft } \times 175 \mathrm { ft }$
B) $150 \mathrm { ft } \times 200 \mathrm { ft }$
C) $360 \mathrm { ft } \times 340 \mathrm { ft }$
D) $125 \mathrm { ft } \times 225 \mathrm { ft }$
E) $350 \mathrm { ft } \times 350 \mathrm { ft }$

Question

Quizplus · Accepted Answer

The maximum floor space for a given perimeter is achieved by a square, because the square has the largest area among all rectangles with a given perimeter. Since the perimeter is 700 ft, each side of the square would be $700 \mathrm { ft } / 4 = 175 \mathrm { ft }$, making the dimensions $175 \mathrm { ft } \times 175 \mathrm { ft }$.

A Company Needs to Build a Warehouse with Perimeter 700ft700 \mathrm { ft }700ft

A Company Needs to Build a Warehouse with Perimeter $700 \mathrm { ft }$