How to Calculate the Length of a Box Given its Surface Area

In this article, we will guide you through the process of calculating the length of a box when you know its surface area, height, and width. This can be particularly useful in various fields such as packaging, construction, and design. We will walk through a practical example using the formula for the surface area of a rectangular box.

Understanding the Problem

Let's consider a rectangular box with the following dimensions:

Height (h 5) cm Width (w 3) cm Surface Area (SA 158) cm2

Surface Area Formula for a Rectangular Box

The formula for the surface area of a rectangular box is:

(SA 2lw 2lh 2wh)

Where:

(SA) is the Surface Area (l) is the Length (w) is the Width (h) is the Height

Solving the Problem

Given the surface area and the dimensions, we can now substitute the known values into the formula:

(158 2l cdot 3 l cdot 5 2 cdot 3 cdot 5)

We simplify this step by step:

Calculate (2 cdot 3 6) Calculate (2 cdot 3 cdot 5 30)

Substituting these values back into the equation:

(158 6l 5l 30)

Simplifying further:

(158 11l 30)

Isolate the term with the unknown variable:

(158 - 30 11l)

Calculate:

(128 11l)

Solve for (l):

(l frac{128}{11} 8) cm

Therefore, the length of the box is 8 cm.

Conclusion

By following the steps provided in this article, you can easily calculate the length of a box given its surface area, height, and width. This method can be applied to any similar problem involving rectangular boxes in real-world scenarios or academic settings.