Question

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

Answer 1

Length of diagonal of cuboid $=\sqrt{l^2+b^2+c^2}$

Surface area of cuboid $=2(lb+bh+hl)$

Assume -

$\Rightarrow length=l$

$Breadth=b$

$Depth=h$

Given eq (1) $l+b+h=19$

eq (2) length of diagonal $=11$

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

Simplifying eq (2)

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

Taking ${(l+b+h)}^2=l^2+b^2+h^2+2lb+2bh+2lh$

substituting values

$\Rightarrow {\left(19\right)}^2=121+2(lb+bh+lh)$

$\Rightarrow 361-121=2(lb+bh+lh)$

$\Rightarrow 240=2(lb+bh+lh)$

$\therefore$ Surface area of cuboid $=240.$