Exercises: Square Roots

The total picture should have a size of $63{\mathrm{cm}}^2$. The area of a single mosaic tile can be calculated by dividing the area of the complete cat picture by the number of tiles.

$\begin{array}{rcl}\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{i}\mathrm{l}\mathrm{e}\mathrm{s}& =& 7\cdot 9\\ & & \\ & =& 63\end{array}$

The cat picture is made up of $63$ mosaic tiles.

$\begin{array}{rcl}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{o}\mathrm{f}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{l}\mathrm{e}& =& \mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{a}÷\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{i}\mathrm{l}\mathrm{e}\mathrm{s}\\ & & \\ & =& 63{\mathrm{cm}}^2÷63\\ & & \\ & =& 1{\mathrm{cm}}^2\end{array}$

A single tile has the size of $1{\mathrm{cm}}^2$.

In order to compute the side length, use the respective formula for the area. Since the tiles are square-shaped, the length is equal to the width.

$\begin{array}{rcl}\mathrm{length}\cdot \mathrm{width}& =& \mathrm{a}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{o}\mathrm{f}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{l}\mathrm{e}\\ & & \\ a\cdot a& =& \mathrm{a}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{o}\mathrm{f}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{l}\mathrm{e}\\ & & \\ a^2& =& 1{\mathrm{cm}}^2\\ & & \\ \sqrt{a^2}& =& \sqrt{1{\mathrm{cm}}^2}\\ & & \\ a& =& 1\mathrm{cm}\end{array}$

For the cat picture, Tina needs mosaic tiles with a side length of $1\mathrm{cm}$.