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?

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