# A rectangular box has two sides whose lengths are 3 centimeters and 9 centimeters and a volume of 135 cm^3. What is the area of its largest side?

Nov 14, 2015

$45 c {m}^{2}$

#### Explanation:

Use the formula $V = a b c$, where V stands for volume and abc stands for different sides.

Let's define our variables:
$V = 135 c {m}^{3}$
$a = 3 c m$
$b = 9 c m$

We want to know how long $c$ is. Therefore, we can rewrite our original formula, by dividing both sides by $a b$:

$V = a b c \to \frac{V}{a b} = \frac{\cancel{a} \cancel{b} c}{\cancel{a} \cancel{b}} \to \frac{V}{a b} = c$

Let's fill in the formula:

$c = \frac{135 c {m}^{3}}{3 c m \cdot 9 c m}$

c=(135cm)^cancel(3)/(27cm^cancel(2)

$c = \frac{135}{27} c m = 5 c m$

To now find the biggest side, we have to multiply $b$ with $c$ (since they are the biggest sides):

$b \cdot c = 9 c m \cdot 5 c m = 45 c {m}^{2}$