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A rectangular carpet has an area of 60 sq. m. Its diagonal and longer side together equal 5 times the shorter side, The length of the carpet is ?
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- 5 m
- 12 m
- 13 m
- 14.5 m
Correct Option: B
Let the longer side = l, shorter side = b and diagonal = d
Then, area of rectangular carpet = l x b = 60 ....(1)
And from question d + l = 5b
⇒ d = 5b - l ...(2)
⇒ d2 = 25b2 + l2 - 10 x lb
⇒ l2+ b2 = 25b2 + l2 - 10 x lb
⇒ l2+b2 = 25b2 + l2 - 10 x 60
⇒ 24b2 = 600
∴ b = √25 = 5 m
√ l = 60 / b = 60 / 5 = 12 m
