Question

The sum of length breadth and height of a cuboid is 25 and its diagonal is 15 cm long find the total surface area of the cuboid

Answer 1

Sum of the dimensions= l+b+h=19

Squaring both sides= (l+b+h)2=(19)2

As,

=>(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

=>l2+b2+h2= (11)2 or 121

Getting back to equation:

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

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

=>Total Surface Area of a Cuboid= 361−121

=240