Question

A square flower garden is surrounded by a brick walkway that is 1.8 m wide. The area of the walkway is equal to the area of the garden. Determine the dimensions of the garden to the nearest tenth of a metre.

Answer 1

The length of the garden is 4.3 m while the width is 4.3 m

Let x represent the length of the garden. Therefore:

The area of the garden = x × x = x²

The width of the walkaway is 1.8 m, hence the length of the garden and walkaway = x + 1.8. The width of the garden and walkaway = x + 1.8.

Hence the area of the garden and walkaway = (x + 1.8) × (x + 1.8) = x² + 3.6x + 3.24

The area of walkaway = (x² + 3.6x + 3.24) - x² = 3.6x + 3.24

Since the area of the walkway is equal to the area of the garden, hence:

3.6x + 3.24 = x²

x² -3.6x - 3.24 = 0

x= 4.34 m or -0.74 m

Since the length cannot be negative, hence x = 4.3  m

Therefore the garden is 4.3 m by 4.3 m

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