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 of height to number of floors

The height \(h = 135\) feet and the number of floors \(n=9\). The ratio is \(\frac{h}{n}=\frac{135}{9}\).

Step2: Calculate the unit rate

Simplify \(\frac{135}{9}=15\). In this situation, the unit rate \(15\) means that each floor of the building is \(15\) feet tall.

Step3: Find the height for 15 floors

Since the height per floor (unit rate) is \(15\) feet, for \(n = 15\) floors, the height \(H=15\times15\).

$$H = 225$$

Answer:

a. The ratio of height of the building to the number of floors is \(\frac{135}{9}\), the unit rate is \(15\) (it means each floor is \(15\) feet tall).
b. \(225\) feet.