The sum of the length, breath and height of a cuboid box is 20 cm and the total surface area of cuboid is 256 sq. cm. What is the maximum length ( in approximate ) of a stick that can be placed inside the cuboid box ?

12 cm

We know that,

Diagonal of cuboid = \(\sqrt {l^2 + b^2 + h^2}\)

We have,

Sum of length, breadth and height = 20 cm

l + b + h = 20

= (l + b + h)² = 400

=  l² + b² + h² + 2(lb + bh + hl) = 400

=  l² + b² + h² + 256 = 400

= l² + b² + h²  = 144

=  \(\sqrt {l^2 + b^2 + h^2}\) = 12