The surface area S of the rectangular solid in the figure is

S = 2(24) + 2(4x) + 2(6x).
Find the length x of the box if the surface area is 248 square centimeters.

248 = 48 + 8x + 12 x

200 = 20 x

x = 10

The three different side areas are 24, 4x = 40 and 6x= 60

The side lengths must be 4, 6 and 10.
The length of the box is 10.

Well, well, well. Let's solve this mathematical riddle, shall we? We have the equation S = 2(24) + 2(4x) + 2(6x) and we're told that S = 248. So, now we just need to substitute the value of S into the equation and solve for x. Let's get to it!

248 = 2(24) + 2(4x) + 2(6x)

First, let's simplify the equation:

248 = 48 + 8x + 12x

Now, let's combine like terms:

248 = 48 + 20x

To isolate x, we need to subtract 48 from both sides:

200 = 20x

And finally, we divide both sides by 20:

x = 10

Voila! The length of the box is 10 centimeters. Ta-da!

To find the length x of the box, we need to solve the equation for the surface area.

Given:

S = 2(24) + 2(4x) + 2(6x)
S = 48 + 8x + 12x
S = 48 + 20x

Now, we are given that the surface area is 248 square centimeters. So, we can substitute S with 248:

248 = 48 + 20x

To solve for x, we can start by subtracting 48 from both sides of the equation:

248 - 48 = 48 + 20x - 48
200 = 20x

Next, we divide both sides of the equation by 20:

200/20 = 20x/20
10 = x

Therefore, the length x of the box is 10 centimeters.

To find the length x of the box, we need to solve the equation for the surface area S, which is given by:

S = 2(24) + 2(4x) + 2(6x)

We are also given that the surface area is 248 square centimeters, so we can set up the equation as follows:

248 = 2(24) + 2(4x) + 2(6x)

Now, we can distribute and simplify the equation:

248 = 48 + 8x + 12x

Combining like terms, we get:

248 = 48 + 20x

Next, we can isolate the variable by subtracting 48 from both sides:

248 - 48 = 48 - 48 + 20x

200 = 20x

Finally, we can solve for x by dividing both sides by 20:

200 / 20 = 20x / 20

10 = x

Therefore, the length of the box is 10 centimeters.