Question

The sum of length, breadth and height of a cuboid is 19 cm and its diagonal is `5sqrt(5)` cm. Its surface area is

Options

• 361 cm²

• 125 cm²

•  236 cm²

• 486 cm²

Answer 1

 236 cm²
Let l, b and h be the length, breadth and height of the cuboid.
Then,

l + b + h = 19

⇒ ( l + b + h )² + 2 (lb + bh + lh) = 36

`⇒ (5sqrt(5) + 2("lb" + "bh" + "lh") = 361`

⇒ 2 (lb + bh + lh) = (361 - 125)

`⇒ 2("lb" + "bh" +"lh") = 236  "cm"^2` 

Hence, the surface area of the cuboid is 236 cm²