UPSC 2015 CDS I Math Paper

Let the length, breadth and height of the cuboid be l, b and h, respectively.
∴l2+b2=132=169....(1)
b2+h2=(√281)2=281....(2)
h2+I2=202=400...(3)
Adding eq (1), (2) and (3), we have
2(l2+b2+h2)=850
⇒l2+b2+h2=425....(4)
From (1) and (4), we have
h2=425−169=256
⇒h=16units
Similarly, l = 12 units andb = 5 units
Therefore, total surface area of thecuboid = 2(lb + bh + hl)
=2(12×5+5×16+16×12)
= 664 square units