Question

The length of the solid diagonal of a cuboid is D units and the sum of the lengths of all its edges is A units then find its total surface area

Answer 1

length of solid diagonal of cuboid = D
sum of all sides = A

let L, B , H are length , width and height of cuboid respectively

we know,
diagonal of cuboid = √(L² + B² + H²)
D = √( L² + B² + H² )
take square both sides
D² = L² + B² + H²

we know, according to algebraic identity, (a + b+ c)²= a² + b² + c² +2(ab +bc+ ca)

use this ,

(L + B + H )² = L² + B² + H² +2(LB +BH +HL)

(A)² = D² +{2(LB +BH + HL)}

surface area of cuboid =2(LB +BH + HL) =A² -D²