Three faces of a cuboid

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

Correct answer:

S =  664

Step-by-step explanation:

d1=13 d2=281=28116.7631 d3=20  d12 = a2+b2 d22 = b2+c2 d32 = a2+c2  a2 = d12  b2 = d12d22+c2 = d12d22+d32a2 2a2 = d12d22+d32  a=2d12d22+d32=213216.76312+202=12   b=2d12+d22d32=2132+16.76312202=5   c=2d12+d22+d32=2132+16.76312+202=16  S=2 (a b+b c+c a)=2 (12 5+5 16+16 12)=664

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