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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