If a rancher has 80 feet of fencing with which to enclose two adjacent rectangular corrals, then for the maximum area the dimensions will be 10 feet and 40/3 feet
From the given figure
4x + 3y = 80 feet
3y = 80 - 4x
y = (80 - 4x) / 3
The area of the rectangle
A = length × width
A = 2x × y
= 2x × (80 - 4x) / 3
Apply distributive property
= (160/3)x - (8/3)x^2
For the maximum area differentiate the values
0 = 160/3 - 16/3x
16/3x = 160/3
x = 160/3 ÷ 16/3
x = 160/3 × 3/16
x = 10 feet
The value of y = (80 - 4x) / 3
y = (80 - 4(10))/3
y = (80-40) / 3
y = 40/3 feet
Therefore, the dimensions are 10 feet and 40/3 feet
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