Application to Real Life Problems
Application to Real Life Problems
IP 3
A piece of wire, \(100\) cm in length is divided into two parts. One part is bent to form a square of side \(x\) cm and the other part a square of side \(y\) cm.
- Express \(y\) in terms of \(x\).
- Show that the total area, \(A\) cm\(^{2}\), of the two squares is given by \(A={{x}^{2}}+{{(25-x)}^{2}}\).
- Calculate the value of \(x\) for which \(A\) has a stationary value. Determine whether this value of \(x\) makes \(A\) a maximum or a minimum. Hence, find the value of \(A\).
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Answer:(a) \(y=25-x\) (b) \(A=x^2+(25-x)^2\) (c) Minimum \(A=\frac{625}{2}\text{ cm}^2\) at \(x=\frac{25}{2}\text{ cm}\)
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