How wide is the floor?

Question

suppose 240 square tiles, each 25cm on a side, are needed to cover a rectangular floor. The floor is 5 meters long. How wide is the floor?

Answer 1

We have a list of information that we can set-up and connect:

240 Square tiles.

Each tile is 25cm long and 25cm wide.

The floor is 5 meters wide.

 

This problem only deals with measurement: width and length, so they can all use the same unit of measurement.

The first thing we need to do is to convert the measurements to all be the same type of measurement: cm into meter or meter into cm.

 

1 Meter = 100cm

So 5 meters = 500cm.

 

Now our list of information is:

240 Square tiles.

Each tile is 25cm long and 25 cm wide.

The floor is 500cm wide.

 

A shape is able to change while keeping the area the same.

The formula for the area of a rectangle is A=l*w (Area = length * width).

So, if we find the total area of the tiles, we can find the total area of the floor, because the tiles are the floor.

 

First, to find the total area for the tiles, we need to know the length and the width.

There are 240 tiles, so if we line up the tiles: 1 tile wide and 240 tiles long, we can then add the measurements of the tiles to have the information to find the area.

 

Each tile is 25cm long and 25cm wide.

1 tile wide = 25cm * 1. So the width of the total area is 25cm in this line of tiles.

240 tiles long = 25cm * 240. So the length of the total area is 6,000cm long in this line of tiles.

The formula for the total area is A=l*w. We are trying to find the area A.

Length = l, so l = 6,000cm. Width = w, so w = 25cm.

6,000cm * 25cm = 150,000cm Squared.

 

The total area of the tiles AND floor is 150,000cm Squared.

 

Now the information we have need is:

The area of the floor is 150,000cm Squared.

The floor is 500cm wide.

The formula for the area is A=l*w.

150,000cm squared = A. 500cm = w. We are looking for l.

 

150,000cm squared = l * 500cm.

If A = l*w, then l = A/w.

l = 150,000cm squared divided by 500cm.

l = 150,000cm squared / 500cm = 300cm.

l = 300 cm.

 

So, the floor is 500cm wide and 300cm long. OR, (if in meters)

 

100cm = 1m

500cm = 5m and 300cm = 3 m.

 

The floor is 5 meters wide and 3 meters long.

Answer 2

How many tiles along the length?

5 meters / 25 cm

500 cm / 25 cm

20

Twenty tiles along the length

 

How many tiles along the width?

240 / 20

12

 

The width of the room is 12(25cm) or 300cm or 3 meters.