Question

Arnold has 24m of fencing to surround a garden, bounded on one side by the wall of his house. What are the dimensions of the largest rectangular garden that he can enclose? Answer is: 12m by 6m though i need to know steps please

Answer 1

if you get one side for free, it is always \(\frac{P}{2}, \frac{P}{4}, \frac{P}{4}\) for the other 3 sides

Answer 2

picture above is not accurate

Answer 3

\[2x+y=24\] and so \(y=24-2x\)
area is \(A=xy=x(24-2x)\)
therefore \[A(x)=24x-2x^2\] max of this quadratic is at the vertex
\[x=-\frac{b}{2a}=-\frac{24}{2\times (-2)}=6\]