# Calculate height or width of rectangle given its area and height or width.

I guess this should be very easy, but I'm stuck.

I have a rectangle:

Area = $520\text{ cm}^2$

$x = 120\text{ cm}$

$y = ?$

So:

Area = $x \cdot y$

$520 \text{ cm}^2 = 120\text{ cm} \cdot y$

And honestly I don't know what to do. If I sqrt everything, result is wrong.

• The thing is "division". Ask yourself, what, when multiplied by 120, gives 520? Commented May 24, 2014 at 8:51

You have the equation, $520 \text{ cm}^2 = 120 \text{ cm} \cdot y$. Now divide both sides by $120 \text{ cm}$.
Step 1: Recall $Area = x . y$
Step 2: Make $y$ the subject of the equation, i.e, divide both side by $x$ $\Rightarrow \frac{Area}{x} = \frac{x.y}{x}$ $\Rightarrow \frac{Area}{x} = y$
So now the formula you need to apply is $y = \frac{Area}{x}$
I guess you became confused with the unit $cm^2$ this is natural, what you need to realize is that the unit of $Area$ is $cm^2$, unit of $x$ is $cm$ and that oof $y$ is $cm$ . so using the formula $Area = x . y$ we have $cm^2 = cm. cm$ now when you apply $y = \frac{Area}{x}$ this affects the unit as follows $cm = \frac {cm^2}{cm}$ which can be simplified to $\Rightarrow cm = \frac {cm . cm}{cm}$ now by cancelling you get $\Rightarrow cm = cm$ , you don't have to do square root in any of the steps.