Question

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

Answer 1

$l+b+h=19$

$Diagonal=11$ $cm$

$\sqrt{l^2+b^2+h^2}=11$

$l^2+b^2+h^2=121$

Now,

$l+b+h=19$

$(l+b+h{)}^2={19}^2$

$l^2+b^2+h^2+2(lb+bh+hl)=361$

$121+2(lb+bh+hl)=361$

$2(lb+bh+hl)=240$

Hence, the surface area of the cuboid is $240$ $c{m}^2$.