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

The sum of length, breadth and height of a cuboid is 19 cm and its diagonal is `5sqrt(5)` cm. Its surface area is 236 cm².

Explanation:

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) = 361

`⇒ (5sqrt(5))^2 + 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.