Question

The sum of the length, breadth and height of a cuboid is $38$ cm the length of its diagonal is $22$ cm. Find the surface area of the cuboid.

Answer 1

Given, $l^2+b^2+h^2={22}^2$ ......(1)
and $l+b+h=38$ .........(2)
Squaring equation (2) on both sides, we get
${(l+b+h)}^2={38}^2$
$\Rightarrow l^2+b^2+h^2+2lb+2bh+2lh={38}^2$
After getting the value from (1), we get
$2lb+2bh+2lh=960$
$\therefore$ surface area of cuboid $=2(lb+bh+lh)=960$