Optional extension A rectangular animal pen is built against a straight wall, so fencing is needed f

Question

Optional extension

A rectangular animal pen is built against a straight wall, so fencing is needed for only three sides. There are $72$ m of fencing. Let each perpendicular side be $x$ m.

Show that the area is $A=72x-2x^2$.[2]
Find the dimensions that maximise the area and hence find the maximum area.[2]

Accepted Answer

(a) $A=72x-2x^2$ (shown). (b) $18$ m by $36$ m; maximum area $648\text{ m}^2$.

Maximum area beside a wall

Maximum area beside a wall

Solution:

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