A family wants to fence in a rectangular area for a garden. one side of the garden will border their house and will not be fenced. find the dimensions of the garden with greatest area that can be enclosed with 80ft of fencing.

Question

Mathematics

Babbles

24 July, 19:45

A family wants to fence in a rectangular area for a garden. one side of the garden will border their house and will not be fenced. find the dimensions of the garden with greatest area that can be enclosed with 80ft of fencing.

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Townsend · Answer 1

Suppose x represents the length of fence perpendicular to the house. Then the area of the garden is

area = x (80 - 2x)

This is the equation of a parabola that opens downward and has its vertex (maximum) at x=20. (The zeros of area=2x (40 - x) are at x=0 and x=40. The vertex is halfway between them.)

The largest rectangular area that can be enclosed is (20 ft) * (40 ft).