Question

Find the length of the diagonal of a cuboid whose length is 20 cm, breath is 12 cm and height is 9 cm .
1 point
15 cm
23 cm
25 cm​

Answer 1

Answer:

Sum of the dimensions :-

l+b+h=19

Squaring both sides-

(l+b+h)2=192

As,

(a+b+c)2=a2+b2+c2+2(ab+bc+ac)

⟹(l+b+h)2=l2+b2+h2+2(lb+bh+lh)

⟹l2+b2+h2+2(lb+bh+lh)=361

As, the diagonal of the cuboid is :-

l2+b2+h2−−−−−−−−−√=11

Transposing:

⟹l2+b2+h2=112 or 121

Getting back to our equation:

l2+b2+h2+2(lb+bh+lh)=361

⟹121+2(lb+bh+lh)=361

⟹2(lb+bh+lh) or Total Surface Area of a Cuboid =361−121 or 240⋅■

Hope I answered your question

Good Luck, Champ!