Methods2025 NHT Exam 2 Section B · Q5CAS active14 marks

Optimising the area of a vegetable garden

David is planning to build a vegetable garden in his backyard, using an existing wall for one side and up to 12 metres of timber for the remaining sides. Assume that David’s backyard is modelled by a flat plane.

a.i.

David considers building a rectangular vegetable garden as shown below, with length $l$ metres and width $w$ metres.

David uses 12 metres of timber for the remaining three sides.

Show that the area of the rectangular vegetable garden, in square metres, can be expressed as $12w - 2w^2$ .

A shaded rectangle against an existing wall along the bottom, with its three timber sides dashed. The side parallel to the wall is labelled l and the two perpendicular sides are each labelled w, with right angles at the wall.

1 mark

Hints, answer checking and worked solutions come with a Season Pass.

a.ii.

Find the maximum possible area of the rectangular vegetable garden.

Give your answer in square metres.

2 marks

Hints, answer checking and worked solutions come with a Season Pass.