the floor of a room is 6 m 30 cm long and 5 m 85 cm wide it is to be paved by square marble stone tiles find the largest size of each tile and hence find the least number of tiles required
Answers
Answer:
Least number of square tiles required is 182.
Largest size of each square tile is 2025 sq.cm.
Step-by-step explanation:
The largest size of each tile is 45 cm long and 45 cm wide.
The least number of tiles required is 182.
Given: The floor of a room is 6 m 30 cm long and 5 m 85 cm wide it is to be paved by square marble stone tiles.
To Find: The largest size of each tile and the least number of tiles required
Solution:
- Whenever we are required to find the largest or greatest value of something, we must calculate the HCF.
- The least number of products = Total value / HCF
Coming to the numerical, we get;
The length of the room is = 630 cm
The breadth of the room is = 585 cm
The area of the room is = ( 630 × 585 ) cm²
= 368550 cm²
We shall find the HCF of the area of the room by the prime factorization method,
630 = 2 × 3 × 3 × 5 × 7
585 = 3 × 3 × 5 × 13
So, the HCF ( 630, 585 ) = 3 × 3 × 5 = 45
Hence, the largest size of each tile is 45 cm long and 45 cm wide.
So, the area of the HCF = ( 45 × 45 ) cm²
= 2025 cm²
Hence, the least number of tiles = Total area / Area of the HCF
= 368550 / 2025
= 182 tiles
Hence, compiling the answers, we get;
The largest size of each tile is 45 cm long and 45 cm wide.
The least number of tiles required is 182.
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