UPSC CDS 2 2021 Math Paper

Let length of the side of the square X be a unit.
Then, p=(a)2=a2‌‌... (i) The length of the side of the bigger square
= The length of diagonal of square X =√2a
∴‌‌q=(√2a)2=2a2 ... (ii)
Now, ‌

p

q

=‌

a2

2a2

‌‌[ from Eq. (i) and Eq. (ii) ]
‌

p

q

=‌

1

2