The sum of the length, breadth and height of a cuboid is $6 \sqrt{3} \mathrm{~cm}$ and the length of

Question

The sum of the length, breadth and height of a cuboid is $6 \sqrt{3} \mathrm{~cm}$ and the length of its diagonal is $2 \sqrt{3} \mathrm{~cm}$. The total surface area of the cuboid is\

Professor PC Thomas Classes · Answer

(c) : Assume length $I$, breadth $b$ and height $h$ of cuboid. 
Given, $l+b+h=6 \sqrt{3} \mathrm{~cm}$ 
Also, $\sqrt{l^{2}+b^{2}+h^{2}}=2 \sqrt{3} \mathrm{~cm}$ 
Squaring (i), we get $(I+b+h)^{2}=108$\ $\Rightarrow \quad l^{2}+b^{2}+h^{2}+2(l b+b h+l h)=108$\ $\Rightarrow \quad 2(l b+b h+l h)=96$ \Area of cuboid is, 2(lb+hb+lh)=96cm$^2$