A farmer has 400 feet of fence with which to fence a rectangular plot of land. The plot lies along a river so that only three sides need to be fenced. Estimate the largest area that can be fenced.
A) $20,000 \mathrm { ft } ^ { 2 }$
B) $24,000 \mathrm { ft } ^ { 2 }$
C) $16,000 \mathrm { ft } ^ { 2 }$
D) $30,000 \mathrm { ft } ^ { 2 }$

Question

A farmer has 400 feet of fence with which to fence a rectangular plot of land. The plot lies along a river so that only three sides need to be fenced. Estimate the largest area that can be fenced. 
A) $20,000 \mathrm { ft } ^ { 2 }$
B) $24,000 \mathrm { ft } ^ { 2 }$
C) $16,000 \mathrm { ft } ^ { 2 }$
D) $30,000 \mathrm { ft } ^ { 2 }$

Quizplus · Accepted Answer

The largest area that can be fenced is achieved when the plot is a rectangle with the length twice the width. If $w$ is the width, then $2w + w = 400$ feet of fencing is used, giving $w = 133.33$ feet. The length is twice the width, so $2w = 266.66$ feet. The area is $w \times 2w = 133.33 \times 266.66 \approx 20,000 \mathrm { ft } ^ { 2 }$.

A Farmer Has 400 Feet of Fence with Which to Fence