UPSC CDS 2 2021 Math Paper

Given, length of the room,
I=21m
breadth of the room, b=16m
and the length of the longest rod that can be placed in the room =29m
We know that, the length of the longest rod that can be placed in the room is the diagonal of the room (cuboid).
We know, diagonal of a cuboid
‌‌=√l2+b2+h2
⇒‌‌29‌‌=√(21)2+(16)2+h2
⇒(29)2‌‌=441+256+h2
⇒‌‌841‌‌=697+h2⇒h2=144
⇒‌‌h‌‌=12cm
Hence, height of the room is 12cm.