2024 CCHY P1 Q10
2024 CCHY P1 Q10
8 marks
The diagram shows an outline of a board, \(ABCDE\), consisting of a rectangle \(ABCE\) of height \(h\) cm and width \(24x\) cm and an isosceles triangle \(CDE\) in which \(CD = DE = 13x\) cm. The perimeter of the board is 480 cm.
- Show that the area of the board, \(A\) cm\(^2\), is given by \(A = 5760x - 540x^2\).[3]
- Calculate the stationary value of \(A\) and determine whether it is a maximum or a minimum.[5]
Solution:
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Answer:(a) \(A=5760x-540x^2\) (shown) (b) Maximum area \(15360\text{ cm}^2\), at \(x=\dfrac{16}{3}\).
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