Certainly! Let's break down the problem step-by-step.
### Part (i) Express the length, breadth, and height of the room in meters.
First, we need to convert the given measurements from meters and centimeters to just meters.
1. Length: 9 meters 80 centimeters
[tex]\[
9 \text{ meters} + 80 \text{ centimeters} = 9.80 \text{ meters}
\][/tex]
2. Breadth: 8 meters 40 centimeters
[tex]\[
8 \text{ meters} + 40 \text{ centimeters} = 8.40 \text{ meters}
\][/tex]
3. Height: 4 meters 20 centimeters
[tex]\[
4 \text{ meters} + 20 \text{ centimeters} = 4.20 \text{ meters}
\][/tex]
So, the room's dimensions in meters are:
- Length: [tex]\( 9.80 \)[/tex] meters
- Breadth: [tex]\( 8.40 \)[/tex] meters
- Height: [tex]\( 4.20 \)[/tex] meters
### Part (ii) Find the highest common factor (HCF) of these three measurements of the room.
To find the HCF, we usually work in whole numbers to make our task easier. Let's convert the measurements to centimeters first, then find the HCF.
1. Length in centimeters:
[tex]\[
9.80 \text{ meters} = 9.80 \times 100 = 980 \text{ centimeters}
\][/tex]
2. Breadth in centimeters:
[tex]\[
8.40 \text{ meters} = 8.40 \times 100 = 840 \text{ centimeters}
\][/tex]
3. Height in centimeters:
[tex]\[
4.20 \text{ meters} = 4.20 \times 100 = 420 \text{ centimeters}
\][/tex]
Now, we find the HCF of 980 cm, 840 cm, and 420 cm.
From calculation (as we have derived from the solution):
- The HCF of 980, 840, and 420 is 140 centimeters.
### Part (iii) What is the longest tape (in meters) which can be used to measure all three dimensions of the room exactly?
To find the longest tape that can measure all three dimensions exactly, convert the HCF from centimeters back to meters.
[tex]\[
140 \text{ centimeters} = 140 / 100 = 1.4 \text{ meters}
\][/tex]
Summary:
1. The dimensions in meters are:
- Length: [tex]\( 9.80 \)[/tex] meters
- Breadth: [tex]\( 8.40 \)[/tex] meters
- Height: [tex]\( 4.20 \)[/tex] meters
2. The highest common factor (HCF) of these dimensions in centimeters is [tex]\( 140 \)[/tex] cm.
3. Thus, the longest tape that can measure all three dimensions exactly is [tex]\( 1.4 \)[/tex] meters long.
