Question

The sum of the length, breadth and height of a cuboid is $19cm$ and the length of its diagonal is $11cm$. Find the total surface area of the cuboid.

Answer 1

Given, the sum of the length, breadth and height of cuboid $=19cm$.
And the length of its diagonal $=11cm$. Let the length, breadth and height of the cuboid be $I,b$ and $h$ respectively.
$\therefore l+b+h=19cm\dots$(i)
and $\sqrt{l^2+b^2+h^2}=11cm\dots$(ii)
Squaring both the sides, we get
$l^2+b^2+h^2=(11{)}^2=121\dots ($ iii $)$
We know that, $(1+b+h{)}^2=[[l^2+b^2+h^2]+2(lb+bh+hl)$
$\Rightarrow (19{)}^2=121+2(lb+bh+hl)$
$\Rightarrow 361=121+2(lb+bh+hl)$
$\Rightarrow 2(lb+bh+hl)=361-121$
$\Rightarrow 2(lb+bh+hl)=240sq.cm$
Hence, the total surface area of cuboid $=240{cm}^2$