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

Answers

  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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