A piece of wire, $12$cm long, is bent to form a rectangle. By letting $x\ \mathrm{cm}$ be the length

Question

A piece of wire, $12$cm long, is bent to form a rectangle. By letting $x\ \mathrm{cm}$ be the length of one side, express the area of the rectangle, $A$cm$^{2}$, in terms of $x$. Find the value of $x$ for which $A$ is the greatest, given that $x$ is an integer. What type of rectangle is this when $A$ is maximum?

Accepted Answer

$x = 3$, square with area 9

Optimizing the Area of a Rectangle Formed from a Fixed-Length Wire

Optimizing the Area of a Rectangle Formed from a Fixed-Length Wire

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