We let x and y be the measures of the sides of the
rectangular garden. The perimeter subtracted with the other side should be
equal to 92.
2x + y = 92
The value of y in terms of x is equal to,
y =
92 – 2x
The area is the product of the two sides,
A
= xy
Substituting,
A
= x (92 – 2x) = 92x – 2x2
Solving for the derivative and equating to zero,
0
= 92 – 4x ; x = 23
Therefore, the area of the garden is,
A
= 23(92 – 2(23)) = 1058 yard2
