1. Rectangle A has length $6 \mathrm{~cm}$ and area $36 \mathrm{~cm}^{2}$.
Rectangle B has length $12 \mathrm{~cm}$ and area $36 \mathrm{~cm}^{2}$.
Rectangle $\mathrm{C}$ has length $9 \mathrm{~cm}$ and area $36 \mathrm{~cm}^{2}$.
The rectangle with the smallest width has a width of $x \mathrm{~cm}$. What is the value of $x$ ?
1. The area of a rectangle is equal to its length multiplied by its width, and so width equals area divided by length.
The width of Rectangle A is equal to $\frac{36 \mathrm{~cm}^{2}}{6 \mathrm{~cm}}=6 \mathrm{~cm}$.
The width of Rectangle B is equal to $\frac{36 \mathrm{~cm}^{2}}{12 \mathrm{~cm}}=3 \mathrm{~cm}$.
The width of Rectangle $\mathrm{C}$ is equal to $\frac{36 \mathrm{~cm}^{2}}{9 \mathrm{~cm}}=4 \mathrm{~cm}$.
The smallest of these widths is $3 \mathrm{~cm}$, and so $x=3$.
(Note that since the three rectangles have the same area, the smallest width would be the one with the largest length.)
ANSWER: $x=3$