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We are given:
Length of the courtyard = 3.78 metres
Width of the courtyard = 5.25 metres
We need to find the largest square tile size (in metres) that can exactly tile the courtyard — i.e., it should be the greatest number that divides both 3.78 and 5.25 exactly.
🟠 Step 1: Convert to centimeters (to avoid decimals)
3.78 m = 378 cm
5.25 m = 525 cm
Now, find the greatest size of square tile (in cm) that exactly divides both 378 and 525.
🟠 Step 2: Find HCF of 378 and 525
Use Euclidean algorithm:
525 ÷ 378 = 1, remainder = 147
378 ÷ 147 = 2, remainder = 84
147 ÷ 84 = 1, remainder = 63
84 ÷ 63 = 1, remainder = 21
63 ÷ 21 = 3, remainder = 0
✅ HCF = 21 cm
🟢 Step 3: Convert back to metres (if needed)
21 cm = 0.21 metres
✔ Final Answer:
The largest size of square tile that can be used is 21 cm or 0.21 metres.