Width of Path Around Rectangular Garden

Consider a rectangular garden that has a length of $24$ meters and a width of $10$ meters. A path of uniform width $x$ meters is built around the garden, increasing both the length and width. The total area of the garden plus the path is $576$ square meters. What is the width of the path?

To solve for $x$, first express the dimensions of the garden plus the path. The new length will be $24 + 2x$ and the new width will be $10 + 2x$. The total area can be expressed as:

$$ (24 + 2x)(10 + 2x) = 576 $$