A floor is covered by 800 tiles measuring 10 cm square.How many square tiles of side 8 cm would be needed to cover the same floor?
area covered by 10 by 10 tiles = 800 x 100 or 80000 cm^2
each 8 by 8 covers 64 cm^2
so number of smaller tiles = 80000/64 = 1250 tiles
Square tiles = 8 × 8 = 64cm^2
Previous tiles = 10 × 10 = 100
Area covered = 100 × 800 = 80000cm^2
No of tiles = 80000÷64 = 1250 tiles
The total area covered is 800 x 10 or 8000 cm2. The new tiles cover 8cm by 8cm, or 8 x 8 = 64 cm2. Simply divide 8000 by 64 to get the answer
To find the number of square tiles with a side length of 8 cm needed to cover the same floor, we need to compare the areas of the tiles.
The area of a 10 cm square tile can be calculated by multiplying the length (10 cm) by the width (10 cm):
Area of 10 cm square tile = 10 cm * 10 cm = 100 cm²
The area of an 8 cm square tile can be calculated using the same formula:
Area of 8 cm square tile = 8 cm * 8 cm = 64 cm²
Now, we can find the ratio of the areas between the 10 cm tiles and the 8 cm tiles:
Area ratio = Area of 10 cm square tile / Area of 8 cm square tile
Area ratio = 100 cm² / 64 cm² = 1.5625
This means that the area of a 10 cm tile is 1.5625 times greater than the area of an 8 cm tile.
To determine the number of 8 cm square tiles needed, we divide the total area covered by the 10 cm tiles (800 tiles) by the area of one 8 cm square tile:
Number of 8 cm tiles = Total area covered by 10 cm tiles / Area of 8 cm square tile
Number of 8 cm tiles = 800 tiles * 100 cm² / 64 cm²
By simplifying the above equation, we find that:
Number of 8 cm tiles = 1250 tiles
Therefore, 1250 square tiles with a side length of 8 cm would be needed to cover the same floor.