Question

if the sum of the length, breadth and depth of a cuboid is 19cm and it's daigonal is 5/5, then it's surface area.

Answer 1

Sum of the dimensions :-

l+b+h=19l+b+h=19

Squaring both sides-

(l+b+h)2=192(l+b+h)2=192

As,

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

⟹(l+b+h)2=l2+b2+h2+2(lb+bh+lh)⟹(l+b+h)2=l2+b2+h2+2(lb+bh+lh)

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

As, the diagonal of the cuboid is :-

l2+b2+h2‾‾‾‾‾‾‾‾‾‾‾‾√=11l2+b2+h2=11

Transposing:

⟹l2+b2+h2=112⟹l2+b2+h2=112 or 121121

Getting back to our equation:

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

⟹121+2(lb+bh+lh)=361⟹121+2(lb+bh+lh)=361

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

Hope I answered your question

Good Luck, Champ!