A city’s building code does not permit building a house that is more than 35 feet tall. An architect working on the design shown at right would like the roof to be sloped so that it rises 10 inches for each foot of horizontal run. (a) Given the other dimensions in the diagram (in feet), will the builder be allowed to carry out this plan? (b) Two vertical supports (shown dotted in the diagram) are to be placed 6 feet from the center of the building. How long should they be?