Exercises: Square Roots

Calculating of the Side Length of the $\text{C}\text{o}\text{l}\text{o}\text{u}\text{r}\text{e}\text{d}\text{S}\text{q}\text{u}\text{a}\text{r}\text{e}$

The formula for the area of a square with side length $a$ reads:

You know that the area of the coloured square has to be $9{\text{ cm}}^2$.

In order to get the side length, you have to find out, which side length becomes $9{\text{ cm}}^2$, when multiplied by itself.

The coloured square has a side length of $a=3\text{ cm}$.

Determining the Perimeter of the Rectangle

The formula for the perimeter of a rectangle with length $l$ and the width $b$ is:

In the figure you can see that the length of the rectangle is 6 times the side length of the square and the width of the rectangle is 4 times the side length of the square.

Now you can substitute the length and the width into the formula for the perimeter of the rectangle. This gives you the solution:

$P_{\text{rectangle}}=2\cdot l+2\cdot b=2\cdot 18\text{ cm}+2\cdot 12\text{ cm}=60\text{ cm}$

The perimeter of the rectangle is thus $60\text{ cm}$.