Three faces of a cuboid

The diagonal of three faces of a cuboid are 13,√281 and 20 units. Then the total surface area of the cuboid is.

Correct result:

S =  664

Solution:

d1=13 d2=281=28116.7631 d3=20  d12=a2+b2 d22=b2+c2 d32=a2+c2  a2=d12b2=d12d22+c2=d12d22+d32a2 2a2=d12d22+d32  a=d12d22+d322=13216.76312+2022=12   b=d12+d22d322=132+16.763122022=5   c=d12+d22+d322=132+16.76312+2022=16  S=2 (a b+b c+c a)=2 (12 5+5 16+16 12)=664



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