Building Roofs

Builders use a ratio to specify the pitch of roofs. For example, a “four:twelve roof” means a roof that rises four units for every 12 units of span – goes up 4 units vertically for every 12 units across horizontally. Suppose a builder whose knowledge of this building convention is faulty, believes that four:twelve means a roof that spans four units for every rise of 12 units. Assume the front of the house is 40 feet across and 20 feet high. Make a scale drawing of what the roof would look like.

(Source: Adapted from Fostering Children’s Mathematical Power. An Investigative Approach to K-12 Mathematics, Arthur J. Baroody, with Ronald T. Coslick, c. 1998 by Lawrence Erlbaum Associates, Mahwah, NJ.)