Surface area of a cuboid is 22 $$cm^2$$ and the sum of the lengths of all its edges is 24 cm. The length of each diagonal of the cuboid, in cm, is

Let length, breadth and height be $$l,b,h$$ cm respectively.

=> Surface area of cuboid = $$2(lb+bh+hl)=22$$ -----------(i)

Sum of all edges = $$4(l+b+h)=24 \Rightarrow (l+b+h)=6$$

Squaring both sides, => $$(l^2+b^2+h^2)+2(lb+bh+hl)=36$$

Substituting value from equation (i), we get :

=> $$(l^2+b^2+h^2)+22=36$$

=> $$(l^2+b^2+h^2)=36-22 = 14$$

$$\therefore$$ Diagonal of cuboid = $$\sqrt{l^2+b^2+h^2}=\sqrt{14}$$

=> Ans - (D)