Question

SUM of length width and height OF CUBICAL BOX IS 19 CM AND LENGTH OF ITS DIAGONAL IS 11 CM ...FIND THE SURFACE AREA OF THE CUBOID BOX???

Answer 1

let the length = l
breadth = b 
height = h

given that l+b+h = 19
and diagonal = 11
⇒$\sqrt{l^2+b^2+h^2}=11$
⇒$l^2+b^2+h^2=121$

We know that
$(l+b+h)^2=l^2+b^2+h^2 + 2(lb+bh+lh)\\ \\ \Rightarrow19^2=121+2(lb+bh+lh)\\ \\ \Rightarrow 2(lb+bh+lh)=361-121\\ \\ \Rightarrow2(lb+bh+lh) = 240$

But 2(lb+bh+lh) is the total surface area or simply "surface area" of the cuboid.
So surface area is 240cm².