Question

1. what is the pitch of the roof of an a - frame building if its height is 3.6 m and its width is 5.4 m? note that the pitch on each side is the same. set up and solve a proportion

Explanation:

Step1: Define pitch and find base - half

The pitch of a roof is the ratio of the rise (height) to the run (half - of the base). The width of the A - frame is 5.4 m, so the run (half - of the base) is $\frac{5.4}{2}=2.7$ m, and the rise (height) is 3.6 m.

Step2: Set up the proportion for pitch

The pitch $p$ is given by the ratio of the rise to the run. So, $p=\frac{3.6}{2.7}$.

Step3: Simplify the ratio

We can simplify $\frac{3.6}{2.7}$ by multiplying both the numerator and denominator by 10 to get $\frac{36}{27}$, and then dividing both by 9. $\frac{36\div9}{27\div9}=\frac{4}{3}$.

Answer:

The pitch of the roof is $\frac{4}{3}$ or 4:3.