A room is 8 m 96 cm by 6 m 72 cm. Find the minimum number of square tiles of the same size needed to cover the floor.
12 tiles
Step 1: Convert all lengths to the same unit (centimetres).
For the length:
\(8\text{ m} = 8\times100 = 800\text{ cm}\)
\(800\text{ cm} + 96\text{ cm} = 896\text{ cm}\)
For the width:
\(6\text{ m} = 6\times100 = 600\text{ cm}\)
\(600\text{ cm} + 72\text{ cm} = 672\text{ cm}\)
Step 2: To use the minimum number of equal square tiles, use the largest possible square side that fits both sides.
This side is the HCF (GCD) of \(896\) and \(672\).
Step 3: Find \(\gcd(896, 672)\) using Euclid’s method.
\(896 = 672 + 224\)
\(672 = 3\times224 + 0\)
So, \(\gcd(896, 672) = 224\text{ cm}\).
Step 4: Find how many tiles fit along each side.
Along length: \(896\div224 = 4\)
Along width: \(672\div224 = 3\)
Step 5: Multiply to get total tiles.
\(4\times3 = 12\)
Answer: 12 square tiles are needed.