The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is $5\sqrt{5}$ cm then its surface area is:

$236cm^2$

l + b + h = 19 cm     -----(1)

Length of diagonal of cuboid = \(\sqrt { l² + b² + h² }\) = 5√5

On squaring both side ,

l² + b² + h² =  125

On squaring equation 1 ,

( l + b + h )² = 19²

l² + b² + h² + 2 ( lb + bh + hl) = 361

125 + 2 ( lb + bh + hl) = 361

2 ( lb + bh + hl) = 236

Total surface are of cuboid = 2 ( lb + bh + hl) = 236 cm²