The width of a container is 5 feet less than its height. its length is 1 foot longer than its height. the volume of the container is 216 cubic feet. how tall is the container?

The height of container is 8 feet

Solution:

Let "w" be the width of container

Let "l" be the length of container

Let "h" be the height of container

The width of a container is 5 feet less than its height

Therefore,

width = height - 5

w = h - 5 ------ eqn 1

Its length is 1 foot longer than its height

length = 1 + height

l = 1 + h ---------- eqn 2

The volume of container is given as:

Given that volume of the container is 216 cubic feet

Substitute eqn 1 and eqn 2 in above formula

Solve by factoring

Use the zero factor principle

If ab = 0 then a = 0 or b = 0 ( or both a = 0 and b = 0)

Therefore,

Also,

Solve by quadratic equation formula

Therefore, on solving we get,

Thus solutions of "h" are:

h = 8

"h" cannot be a imaginary value

Thus the solution is h = 8

Thus the height of container is 8 feet

step-by-step explanation:

b and c