Question

Craig has 60 feet of fencing with which to make a rectangular garden area. One side of the rectangular garden will be the side of the Craig’s house. Find the length and width for a maximum garden area

1. The length and width for a maximum garden area is 15 feet by 30 feet.

### What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables. An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.
Let x represent the side parallel to Craig’s house and y represent the other side. One side of the rectangular garden will be the side of the Craig’s house. Hence:
2x + y = 60
y = 60 – 2x      (1)
Area (A) = xy = x(60 – 2x)
A = 60x – 2x²
The maximum area is at A’ = 0, hence:
A’ = 60 – 4x
60 – 4x = 0
x = 15
y = 60 – 2(15) = 30
The length and width for a maximum garden area is 15 feet by 30 feet.
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