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

Answer:

3 feet wide and 9 feet long.

Step-by-step 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, $3W^2=27 \Rightarrow W^2=\frac{27}{3}=9 \Rightarrow W=\sqrt{9}=3ft$

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