College Math

posted by Sarah

5) A landscaper wants to make a small planter and surround it with edging material for a client. She is deciding between two designs.
Design 1: A square planter
Design 2: A circular planter
Edging material costs $4 per ft. for the straight variety which she would use for Design 1 and $5 per foot for the flexible variety which she would use for Design 2.

a. If she decides on a perimeter of 24 ft. Which design would give her the larger planting area?
b. If she decides to spend $120 on edging material, which Design would give her the larger planting area?

  1. Steve

    (a) a circle always gives the largest area for a given perimeter.

    Among rectangles, a square gives the largest area.

    (b)
    1: p = 120/4 = 30 ft
    area: 7.5^2 = 56.25
    2: c = 120/5 = 24
    area: = 45.8
    So, the expensive fencing reduces the circular area for planting.

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