Question

A farmer has 2400ft of fencing and wants to fence off arectangular field that borders a straight river. He doesn't needfencing along the river. What are the dimensions of the fieldthat has the largest area?800 ft by 300ft1200 ft by 1200 ft600 ft by 1200 ft700 ft by 1000 ft

Answer 1

Solution:

Given:

$F\text{encing of 2400 ft}$

The fenced part of the field must add up to 2400ft.

The possible fencing of the field if the fencing along the river is not needed are shown below;

Possibility 1:

Possibility 2:

From the two possible scenarios, to get the dimensions of the field with the largest area,

$\begin{gathered} \text{Area of a rectangle=length x breadth} \\ A=l\times b \\ \text{For case 1:} \\ l=600ft \\ b=1200ft \\ A_1=600\times1200 \\ A_1=720,000ft^2 \\ \\ \\ \\ \text{For case 2:} \\ l=700ft \\ b=1000ft \\ A_2=700\times1000 \\ A_2=700,000ft^2 \\ \\ \text{Hence, } \\ A_1>A_2,\text{ 720,000 square fe}et\text{ is larger.} \end{gathered}$

Therefore, the dimension of the field with the largest area is 600ft x 1200ft