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:
Answer & explanation
Correct answer: option 1
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