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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
Solution
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
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