a rectangle carpet has an area of 120 sq metres and..., Area, General Mathematics

Question:A rectangle carpet has an area of 120 sq. metres and a perimeter of 46 metres. The length of its diagonal is :

A `15 m` 
B `16 m` 
C `17 m` 
D `20 m`

/98

+ AnswerC

+ ExplanationLet length = a metres and breadth = b metres.

Then,` 2 (a + b) = 46 or a + b`

    = 23. also, ab = 120

  :. Diagonal` = sqrt(a^2 + b^2)`

                   `= sqrt(a + b)^2 - 2ab`

                `= sqrt((23))^2 - 240`

                `= sqrt(289)`

                `= 17 m`

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