A box with a height of 2 centimeters has a volume of 24 cubic centimeters. The length is three times longer that its width. What is the length of the box?
Let w = width
2w * 3w = 24
6w^2 = 24
w^2 = 24/6
w^2 = 4
W = 2
To find the length of the box, we need to use the formula for the volume of a rectangular box, which is:
Volume = Length x Width x Height
We are given the height of the box as 2 centimeters and the volume as 24 cubic centimeters. We also know that the length is three times longer than the width.
Let's assign a variable to the width of the box. Let's say "w" represents the width.
Since the length is three times longer than the width, we can express the length as 3w.
Now we have the following equation:
24 = (3w) x w x 2
To simplify the equation, we can multiply the terms:
24 = 6w^2
Divide both sides of the equation by 6:
4 = w^2
Now, take the square root of both sides to find the value of w:
√4 = √(w^2)
2 = w
So, the width of the box is 2 centimeters.
To find the length, we substitute the value of the width into the expression for length:
Length = 3w = 3 x 2 = 6 centimeters.
Therefore, the length of the box is 6 centimeters.