A sandbox in the shape of a rectangular prism is 12ft. high and needs to contain at least 42 ft.3 of sand. How would you write an inequality to express the possible area of the base, b , of the sandbox?

Answer 1

The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.

Given that the height is 12ft and the volume needs to be at least 42 ft^3, we can write:
V = lwh ≥ 42

Substituting in the given height of 12ft:
(12)(l)(w) ≥ 42

Simplifying:
12lw ≥ 42

To solve for the possible area of the base, b (which is equal to lw), divide both sides by 12:
lw ≥ 42/12
lw ≥ 3.5

Therefore, the inequality that expresses the possible area of the base, b, of the sandbox is b ≥ 3.5.