Question

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

Answer 1

l +b + h= 19


Length of diagonal
$\sqrt{l {}^{2} + b {}^{2} + } h {} ^{2} = 11$
l^2 +b^2 +h^2 =121..............(1)


l + b + h =19

Squareing both sides

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


2(lb + lh +bh) = 361 - 121

= 240