UPSC CDS 1 2022 Math Paper

Formula used:
Area of square =(‌ side ‌)2
Diagonal =√‌2×( side )
Calculation:
Let a nad A be the side of n identical square and large square.
Diagonal of square =A√‌2
⇒A√‌2=m
⇒A=m∕√‌2
Area of large square = sum of the area of small square
⇒A2=n×a2
⇒m2∕2=n×a2‌‌[∵A=m∕√‌2]
⇒a=m∕√(2n)
∴ The side of the smaller square sheet is m∕√‌(2n).