Answer:
- The length of each side of the rug is 3m
- 4 rugs are need to cover an area of 36m²
- The space between them is 1m
Step-by-step explanation:
Given
Area of a square rug = 9m²
Required
- Length of each side of the rug?
- Number of rugs needed to cover an area of 36m²
- Space between the rug and an area of 16m²
Calculating the side of the rug
Given that the rug is a square rug;
The area of a square is calculated thus;
[tex]Area = Length * Length[/tex]
[tex]Area = Length^2[/tex]
By Substituting 9 for Area; we have
[tex]9 = Length^2[/tex]
Take square root of both sides
[tex]\sqrt{9} = \sqrt{Length^2}[/tex]
[tex]3 = Length[/tex]
[tex]Length = 3[/tex]
Hence, the length of each side of the rug is 3m
Calculating the number of rugs needed to cover an area of 36m²
The number of rugs needed is calculated by dividing the area to be covered (36m²) by area of the rug (9m²)
Mathematically,
Number of rugs = [tex]\frac{36m^2}{9m^2}[/tex]
Number of rugs = [tex]4[/tex]
Hence, 4 rugs are need to cover an area of 36m²
Calculating the space between the rug and an area of 16m²
First, the length of the sides of the area needs to be calculated
The area of a square is calculated thus;
[tex]Area = Length * Length[/tex]
[tex]Area = Length^2[/tex]
By Substituting 16 for Area; we have
[tex]16 = Length^2[/tex]
Take square root of both sides
[tex]\sqrt{16} = \sqrt{Length^2}[/tex]
[tex]4 = Length[/tex]
[tex]Length = 4[/tex]
Hence, the length of each side of the room is 4m
Recall that the length of each side of the rug is 3m
Provided that the rug is at the middle of the room.
The space between them is calculated as Length of the room - Length of the rug
Space = 4m - 3m
Space = 1m
Hence, the space between them is 1m
