Question

Suppose you are an elementary school teacher. You want to order a rectangular bulletin board to mount on a classroom wall that has an area of 90 square feet. Suppose fire code requirements allow for no more than 30% of a classroom wall to be covered by a bulletin board. If the length of the board is three times as long as the width, what are the dimensions of the largest bulletin board that meets fire code?

Answer 1

3 feet wide and 9 feet long.

Explanation:

The classroom wall has an area of
`90ft^2`.

The fire code requirements allow a bulletin board with an area of at most 30% of
`90ft^2`. This means that the maximum area of the bulletin board is
`27ft^2`

Let L and W be the length and wide of the bulletin board.

If the length of the board is three times as long as the width, then L=3W, and the area of the board is
`LW=3WW=3W^2`

For the largest board we have,
`3W^2=27 \Rightarrow W^2=(27)/(3)=9 \Rightarrow W=√(9)=3ft`

So, the largest bulletin board that meets the fire code is 3 ft. wide and 9 ft. long.