The volume of a box(v) varies directly with its length(l). if a box in the group has a length of 30 inches, and the girth of 20 inches (perimeter of the side formed by the width and height), what is its height? use k = 24. (hint: volume = length width height. solve for length, and substitute into the equation for constant of proportionality.) inches or inches

Volume of box (V) is given by:

           .....[1]

where,

l is the length , w is the width and h is the height of the box respectively.

As per the statement:

The volume of a box(V) varies directly with its length(l).

then;

where, k is the constant of proportionality.

Substitute  k = 24 and l = 30 inches we have;

Substitute the given values of V  and l in [1] we have;

Divide both sides by 30h we have;

              .....[2]

It is also given that  the girth of 20 inches (perimeter of the side formed by the width and height)

Perimeter of rectangle formed by width and height is given by:

P = 2(w+h)

then;

Divide both sides by 2 we have;

or

w+h = 10                   .....[3]

Substitute equation [2] into [3] we have;

⇒

⇒

⇒

⇒

Take h-6 common we have;

⇒

By zero product property we have;

h-6=0 or h-4=0

⇒h = 6 inches or h =  4 inches.

therefore, the height is,  6 or 4 inches

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