Question

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

• A. $240{cm}^2$
• B. $200{cm}^2$
• C. $210{cm}^2$
• D. $340{cm}^2$

Answer 1

The correct option is A $240{cm}^2$

$l+b+h=19⟶\left(1\right)\sqrt{l^2+b^2+h^2}=11l^2+b^2+h^2=121⟶\left(2\right)$
from (1), $l+b+h=19$
${(l+b+h)}^2={19}^2=361l^2+b^2+h^2+2(lb+bh+hl)=361121+2(lb+bh+hl)=361$[from(2)]
$2(lb+bh+hl)=240$
therefore, surface area of cuboid is $240c{m}^2$