Question

The sum of length, breadth and height of a cuboid is $38cm$ and the lengths of its diagonal is $22cm$. Find the total surface area of the cuboid (in $c{m}^2$).

Answer 1

Let be length $=l$, breadth $=b$, height $=h$
According to question,
$l+b+h=38$
Squaring both side, we get,
$(l+b+h{)}^2={38}^2$
$\Rightarrow l^2+b^2+h^2+2lb+2bh+2lh=1444$ .....$\left(i\right)$
Diagonal of cuboid $=\sqrt{l^2+b^2+h^2}$
$\sqrt{l^2+b^2+h^2}=22$
Squaring both side, we get
$l^2+b^2+h^2=22\times 22=484$
Put the value $l^2+b^2+h^2$ in equation $\left(i\right)$, we get
$484+2(lb+bh+lh)=1444$
$\Rightarrow 2(lb+bh+lh)=1444-484$
$\therefore$ Total surface area of cuboid $=960c{m}^2$