a rectangle carpet has an area of 60 sq m if..., Area, General Mathematics

Question:A rectangle carpet has an area of 60 sq.m. If its diagonal and longer side together equal 5 times the shorter side, the length of the carpet is :

A `5 m` 
B `12 m` 
C `13 m` 
D ``14.5 m`

/98

+ AnswerB

+ ExplanationLet, length = x metres and breadth = y metres.

Then, xy = 60 and `sqrt(x^2 + y^2 + x = xy`

 :. xy = 60 and` (x^2 + y^2) = (5y - x^2)`

  or xy = 60 and` 24y^2 - 10xy = 0`

`:. 24y^2 - 10 xx 60 = 0 or y^2`

`= 25 or y = 5`

`:. x = (60/5) m`

= 12 m. So, length of the carpet = 12 m.

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