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Allotment Areas

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A citizen wants to reduce their carbon footprint, so decides to grow their own produce in their garden.
The area set out for growing vegetables is shown below, and they want to place a shed in the area marked A.

Allotment Areas diagram

Given that all dimensions are given in metres, and the total area of the plot is 65㎡ , find the values of \(x \) and \(y \) and hence the depth and width of the shed that they need to purchase.

[6 marks]

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