# 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.

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The thing is "division". Ask yourself, what, when multiplied by 120, gives 520? – Shubham May 24 '14 at 8:51

You have the equation, $520 \text{ cm}^2 = 120 \text{ cm} \cdot y$. Now divide both sides by $120 \text{ cm}$.

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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.

If you are confused with units of problems like this, plug the units in the formula you are using and simplify, if your method is correct, unit at right side should be equal to the unit on the left side.

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