A package with square ends has combined length and girth(girth is perimeter of a cross section) of 120 in. The surface area of the entire package is 3600 sq. in.

Determine the dimensions of the package.
s in. * s in.* l in.
One solution is: 11.08in. * 11.08in. * 75.68in. Find the other solution
Hint: if 4s+length=120 then length=120-4S
Round your answer to 2 decimals. Enter the 3 dimensions separated by commas

To determine the other solution for the dimensions of the package, we can use the given information and the hint provided.

Let's assume the side length of the square ends is 's' inches, and the length of the package is 'l' inches.

According to the given information, the combined length and girth of the package is 120 inches. The girth of a square end is equal to the perimeter, which is 4s inches. So, we can write the equation:
4s + l = 120

The surface area of the entire package is given as 3600 square inches. The surface area of a rectangular prism can be calculated using the formula: 2lw + 2lh + 2wh. In this case, the surface area is given as 3600 square inches. Since the square ends have the same dimensions, the surface area can also be expressed as 2s^2 + 2sl:
2s^2 + 2sl = 3600

Now we have a system of two equations with two variables. We can solve this system to find the values of 's' and 'l'.

Using the first equation, we can isolate 'l':
l = 120 - 4s

Substituting this value of 'l' into the second equation, we get:
2s^2 + 2s(120 - 4s) = 3600
2s^2 + 240s - 8s^2 = 3600
-6s^2 + 240s - 3600 = 0

Dividing the equation by -6 to simplify it, we get:
s^2 - 40s + 600 = 0

Solving this quadratic equation using factoring or the quadratic formula, we find that the solutions are s = 10 and s = 60/11 ≈ 5.45.

Now we can substitute these values back into the first equation to find the corresponding lengths:
For s = 10:
l = 120 - 4(10) = 80
So the dimensions for this solution are: 10 in. * 10 in. * 80 in.

For s ≈ 5.45:
l = 120 - 4(5.45) ≈ 98.2
So the dimensions for this solution (rounded to 2 decimals) are: 5.45 in. * 5.45 in. * 98.2 in.

Therefore, the other solution for the dimensions of the package is approximately 5.45 in. * 5.45 in. * 98.2 in.

looks like you defined s to be the measure of each of the sides of the end.

let the length be l
so girth = 4s + l = 120

total area = 2s^2 + 4 sl = 3600
s^2 + 2sl = 1800
s^2 + 2s(120-4s) - 1800 = 0
s^2 + 240s - 8s^2 - 1800=0
7s^2 - 240s +1800 = 0

by the formula
s = (240 ± √7200)/14
s = 11.08 or s = 23.20

if s=23.20 , then l = 120-4(23.20) = 27.18

23.20 , 23.20 , 27.18