EXPLANATION
Let's see the facts:
Length = 4*longer leg
Shorter leg of the base= 1/2 longer leg
We know that Volume = 5832 = 1/2* length* longer leg* shorter leg
Let's call x to the longer leg, the variables are:
length= 4*longer leg= 4x --> x is the longer leg
Shorter leg= 1/2longer leg= 1/2x --> x is the longer leg
Substituting terms, the equation would be:
[tex]5832=\frac{1}{2}\cdot4x\cdot x\cdot\frac{1}{2}x[/tex]Multiplying like terms:
[tex]5832=\frac{4}{4}x^3[/tex]Simplifying:
[tex]5832=x^3[/tex]Switching sides:
[tex]x^3=5832[/tex]Isolating x:
[tex]x=\sqrt[3]{5832}[/tex]Solving the cubic root:
[tex]x=18[/tex]So, x is the value of the longer leg.
Now, we need to find the length, we know that length=4*longer leg
So, the length of the carton is 4*18= 72
The answer is 72
