the sum of the length breadth and depth a cuboid is..., Area & Volume, General Mathematics

Question:The sum of the length, breadth and depth of a cuboid is `19` cm and its diagonal is `5√5 cm`. Its surface area is :

A `361 cm^2` 
B `125 cm^2` 
C `236 cm^2` 
D `486 cm^2`

/113

+ AnswerC

+ Explanation`(1 + b + h) `

`= 19 & √1^2 + b^2 + h^2`

`= 5√5 and so (1^2 + b^2 + h^2)`

`= 125`

Now`(1 + b + h)^2 = 19^2`

`⇒ (1^2 + b^2 + h^2) + 2 (1b + bh + 1h) = 361`

`⇒ 2 (1b + bh + 1h)`

`= (361 - 125)`

`= 236`.

:. Surface area

`= 236 cm^2.`

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