Question

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?

Answer 1

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