Question

A gardener is planning to build a flower bed with two equally-sized sections. The gardener will use a total of 36 feet of wood to surround both sections of the flower bed. The diagram shows the flower bed. create an equation to represent this situation.

Answer 1

The equation representing the situation is;

36 = 3·y + 4·x

Explanation:

The structures the gardener is planning to build = Equally-sized sections of flower bed

The length of wood the gardener has to surround both gardens = 36 feet

The perimeter of the entire garden, P = 2·y + 2 × 2·x

The length of the wood separating the two gardens = The length of the side 'y'

The perimeter of the garden and the length of the fence separating the two gardens = P + y = 2·y + 2 × 2·x + y = 3·y + 4·x

Therefore the length of wood available, 36 feet, will be used for a length equivalent to P + y

∴ 36 = P + y = 3·y + 4·x

∴ 36 = 3·y + 4·x

The equation representing the situation is 36 = 3·y + 4·x.