The sum of length, breadth and depth of a cuboid is `19\ c m` and length of its diagonal is `11\ c mdot` Find the surface area of the cuboid.

Answer

`240 cm^(2)`

Explanation

`(l + b + h) = 19 cm and sqrt(l^(2) + b^(2) + h^(2)) = 11 cm`
`rArr (l + b + h)^(2) = 361 cm^(2) and (l^(2) + b^(2) + h^(2)) = 212 cm^(2)`
`rArr (l^(2) + b^(2) + h^(2)) + 2 (lb + bh + lh) = 361 cm^(2) and l^(2) + b^(2) + h^(2) = 121 cm^(2)`
`rArr 212 cm^(2) + 2(lb + bh + lh) = 361 cm^(2)`
`rArr 2(lb + bh + lh) = (361 - 121) cm^(2) = 240 cm^(2)`