Applications of Parabolas
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The two shorter sides of a right-angled triangle add up to \(14\) cm. Let one of these sides be \(x\) cm.
(a) Show that the area of the triangle is \(A = \tfrac{1}{2}x(14 - x)\) cm\(^2\).
(b) Find the value of \(x\) that gives the greatest area, and find this area.
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