The diagram shows a plan for a rectangular piece of land ABCD AD 40 metres Vegetables are going to be planted in the triangular vegetable patch ACP BP CD x metres a) Show that the area, A m of the vegetable patch is given by A 20x 1 2x 2 b) Given that x can vary, find the maximum area of the vegetable patch, showing clearly that A is a maximum not a minimum B A X P 40 X D

Question: The diagram shows a plan for a rectangular piece of land ABCD. AD = 40 metres. Vegetables are going to be planted in the triangular

The diagram shows a plan for a rectangular piece of land ABCD. AD = 40 metres. Vegetables are going to be planted in the triangular vegetable patch ACP. BP = CD= x metres.

a) Show that the area, A m² of the vegetable patch is given by
A = 20x −1/2x².

b) Given that x can vary, find the maximum area of the vegetable patch,
showing clearly that A is a maximum not a minimum.

B A -X P 40 X D

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