step by step answer
Answers
Answer:
answer is 110
Step-by-step explanation:
because 2(L+B)
=2(9+6)
=2(15)
=30
=30+(20×4)
=30+80
=110
Given :-
The dimensions of a rectangular floor are 9 m and 6 m
The dimensions of tiles laid down in the given pattern are 40 cm and 10 cm
Width of the path is 20 cm
To find :-
The number of tiles .
Solution :-
Given that
The dimensions of the rectangular floor are 9 m and 6 m
We know that
1 m = 100 cm
6 m = 600 cm
9 m = 900 cm
Let l = 900 cm
Let b = 600 cm
Width of the path (w) = 20 cm
We noticed that The path contains two rectangle and one square .
Area of a rectangle = length × breadth sq.units
Area of a rectangle whose length 900 cm and breadth 20 cm
= 900 cm × 20 cm
= 18000 cm²
Area of a rectangle whose length 600 cm and breadth 20 cm
= 600 cm × 20 cm
= 12000 cm²
We know that
Area of a square is side×side sq.units
Area of square whose side is 20 cm
= 20 cm × 20 cm
= 400 cm²
Area of the path = Area of two rectangles - Area of the square
= 18000 + 12000 - 400
= 30000 - 400
= 29600 cm²
The dimensions of a tile = 40 cm and 10 cm
Area of the tile = 40 cm × 10 cm = 400 cm²
Let the number of tiles required be X
Total area of X tiles = 400X cm²
We have,
400 X = 29600
=> X = 29600/400
=> X = 296/4
=> X = 74
Therefore, Required tiles = 74
Alternative Method :-
We know that
If two perpendicular paths of uniform width (w) run inside a rectangle ,one parallel to the length and other parallel to the breadth then Area of the path = w(l+b-w) sq.units
We have,
l = 900 cm
b = 600 cm
w = 20 cm
Area of the path = 20(900+600-20) cm²
=> 20(1500-20)
=> 20(1480) cm²
=> 29600 cm²
Area of the path = 29600 cm²
The dimensions of a tile = 40 cm and 10 cm
Area of the tile = 40 cm × 10 cm = 400 cm²
Let the number of tiles required be X
Total area of X tiles = 400X cm²
We have,
400 X = 29600
=> X = 29600/400
=> X = 296/4
=> X = 74
Therefore, Required tiles = 74
Answer :-
The required number of tiles are 74
Used formulae:-
♦ Area of a rectangle = length × breadth sq.units
♦ Area of a square is side×side sq.units
♦ If two perpendicular paths of uniform width (w) run inside a rectangle ,one parallel to the length and other parallel to the breadth then Area of the path = w(l+b-w) sq.units