When builders construct or remodel a house, it is incredibly important that they follow certain standards. These rules, typically called building codes, help ensure that homes are built safely—that they're unlikely to collapse or fall apart. Roofers and carpenters often use ratios and proportions to figure out how to construct a building "to code" while following the plans provided by the architect.
When builders construct a pitched roof, they typically give it a pitch of 1:3 as a rise to span ratio. Knowing this ratio is helpful if you need to calculate the overall size of the roof. For each meter the roof rises, it must span 3 meters.
Suppose the span or width of a roof is 5.4 meters. What is the total rise of the roof if the pitch is designed with a 1:3 rise to span ratio? In your notebook, write a proportion to answer this question, and solve for the total rise. Then click the button below to check your work.
| Let x equal to rise of the roof. | \(\mathsf{ \frac{1}{3} = \frac{x}{5.4} }\) |
| Now cross multiply. | \(\mathsf{ 3x = 5.4 }\) |
| Solve the equation for x. | \(\mathsf{ x = 1.8 }\) |
The rise of the roof is 1.8 meters.
