If the sum of three dimensions and the total surface area of a rectangular box are 12 cm and 94 cm^2 respectively, then the maximum length of a stick that can be placed inside the box is

Explanation:

Let length = l,

breadth = b, height = h

given that

(l+b+h)=12cm

= total surface area of box

=2(lb+bh+hl)

⇒94m^2(given)

(l+b+h)^2

⇒l^2+b^2+h^2+2(lb+bh+hl)

(12)^2=l^2+b^2+h^2+94

144−94⇒l^2+b^2+h^2

⇒50=l^2+b^2+h

diagonal of box =√l^2+b^2+h^2

∴ Length of longest rod that can be put inside the box

=√l^2+b^2+h^2

=5√2cm