Question

A rectangular box has sides 3,4 , and \(x\) and a volume of 18 . What is the value of \(x\) ?

Short answer

The value of x is \(\frac{3}{2}\).

Step-by-step solution

Write the equation for the volume of the rectangular box

The equation for the volume of the rectangular box is: Volume = length * width * height In our case: 18 = 3 * 4 * x

Simplify the equation

First, we can simplify the equation by multiplying 3 and 4: 18 = 12 * x

Solve for x

Now, we need to solve for x. To do this, we can divide both sides of the equation by 12: \(x = \frac{18}{12}\)

Simplify the fraction to get the value of x

To simplify the fraction, we can reduce it to the lowest terms: \(x = \frac{18}{12}= \frac{3\cdot6}{3\cdot4}\) \(x = \frac{3}{2}\) Therefore, the value of x is \(\frac{3}{2}\).