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A shipping carton has the shape of right triangular prism. Thelength of the carton is 4 times the longer lag of the righttriangular base. The shorter leg of the base is 1/2 of the longerleg. If the volume is 5832 cubic inches what is the length of thecarton?

A shipping carton has the shape of right triangular prism. Thelength of the carton-example-1

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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:


5832=(1)/(2)\cdot4x\cdot x\cdot(1)/(2)x

Multiplying like terms:


5832=(4)/(4)x^3

Simplifying:


5832=x^3

Switching sides:


x^3=5832

Isolating x:


x=\sqrt[3]{5832}

Solving the cubic root:


x=18

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

User Harshit Kumar
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