Question

1. use patterns and structure the height of a building is proportional to the number of floors. the figure shows the height of a building with 9 floors. a. write the ratio of height of the building to the number of floors. then find the unit rate, and explain what it means in this situation. b. how tall would the building be if it had 15 floors?

Explanation:

Step1: Find the ratio

The ratio of height of the building to the number of floors is $\frac{h}{n}$. Given $h = 135$ feet and $n=9$ floors, the ratio is $\frac{135}{9}$.

Step2: Simplify the ratio (find unit rate)

Simplify $\frac{135}{9}=15$. The unit rate of 15 means that each floor of the building is 15 feet tall.

Step3: Find height for 15 - floor building

If each floor is 15 feet tall and there are $n = 15$ floors, then the height $H$ of the 15 - floor building is $H=15\times15$.
Calculate $15\times15 = 225$.

Answer:

The ratio of height of the building to the number of floors is $\frac{135}{9}$. The unit rate is 15, which means each floor is 15 feet tall. A 15 - floor building would be 225 feet tall.