



 
Hi Lexie, Suppose that the length of the garden in $L$ meters and the width is $W$ meters. Since the perimeter is the distance all the way around the garden the perimeter $P$ is given by \[P = 2L + 2W \mbox{ meters}\] and the area $A$ is given by \[A = L \times W \mbox{ square meters.}\] You know that the perimeter is 24 meters we have \[2L + 2W = 24 \mbox{ meters.}\] solve this equation for $L$ and substitute into the equation for the area $A.$ This gives an equation for $A$ in terms of $W.$ What you do at this point depends on what you know. If you are studying calculus you can use calculus to find the value of $W$ that maximizes $A.$ Or you can notice that the equation for $A$ in terms of $W$ is a quadratic in $W$ so its graph is a parabola and you can use properties of the parabola to determine the maximum value of $A$ and the value of $W$ that gives this maximum. Write back if you need more assistance, Penny 



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