The diagram below shows a square $PQRS$ of side $4$ cm. $T$ is a point on $PQ$, $x$ cm fro

Question

The diagram below shows a square $PQRS$ of side $4$ cm. $T$ is a point on $PQ$, $x$ cm from $Q$ and $U$ is a point on $PS$, $x$ cm from $S$. Show that the area $A$, of the quadrilateral $TRSU$, is given by $A = 8 + 2x - \frac{1}{2}x^2$. Find the value of $x$ that makes $A$ a maximum. Find the maximum value of $A$.

Accepted Answer

(a) $A=8+2x-\frac12x^2$ (b) $x=2\text{ cm}$ (c) $A_{\max}=10\text{ cm}^2$

Differentiation - Problems Involving Maximisation and Minimisation

Differentiation - Problems Involving Maximisation and Minimisation

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