Question

The height of a building (135) is proportional to the number of floors The figure shows the height of a building with 9 floors. 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. How tall would the building be if it had 15 floors?

Answer 1

Part a) The ratio is
`(135)/(9)(ft)/(floors)`

Part b) The unit rate means that each floor of the building has a height of 15 feet

Part c) 225 ft

Explanation:

Part a)

see the attached figure to better understand the problem

Let

x -----> the height of the building in feet

y ----> the number of floors

The ratio of the height of the building to the number of floors is equal to divide the height of the building by the number of floors

`ratio=(x)/(y)`

we have

`x=135\ ft\\y=9\ floors`

substitute

`ratio=(135)/(9)(ft)/(floors)`

Part b)

The unit rate is

`(135)/(9)(ft)/(floors)=15(ft)/(floor)`

That means -----> Each floor of the building has a height of 15 feet.

Part c) How tall would the building be if it had 15 floors

Let

x ----> the height of the building

using proportion

`(1)/(15)(floor)/(ft)=(15)/(x)(floor)/(ft)\\\\x=15(15)\\\\x=225\ ft`