Quadratic Functions, Equations and Inequalities

Quadratic Functions, Equations and Inequalities

Secondary 3

A farmer has \(40\text{ m}\) of fencing for three sides of a rectangular enclosure. The fourth side lies along a straight wall and needs no fencing.

  1. Express \(L\) in terms of \(x\), and state the domain of \(x\).

  2. Form an expression for the area \(A\).

  3. Find the maximum area and the enclosure’s dimensions.

Solution:

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Answer:(a) \(L=40-2x,\ 0<x<20\); (b) \(A=-2(x-10)^2+200\); (c) Maximum \(200\text{ m}^2\), Dimensions \(10\text{ m}\times20\text{ m}\).

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