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.