Question

A raised garden is a rectangular prism with a width of 60 in. And a length that is three times the height "h". The volume of the garden is 103,680 in^3. In inches, what is the height of the raised garden?

Answer 1

24 in

Explanation:

From the question,

The formula for finding the volume of a rectangular prism is

V = l×w×h...................... Equation 1

Where l = length, w = width, h = height.

From the question, we were told that the length of the prism is three times the height.

i.e,

l = 3h....................... Equation 2

Substitute equation 2 into equation 1

V = 3h×w×h

V = 3h²w............... Equation 3

Given: V = 103680 in³, w = 60 in

Substitute these values into equation 3 and solve for h

103680 = 3(h²)(60)

103680 = 180h²

h² = 103680/180

h² = 576

h =
`√(576)`

h = 24 in.

Hence the height of the raised garden is 24 in