If the perimeter of a rectangular plot is 34 metres and its area is 60

1.	If the perimeter of a rectangular plot is 34 metres and its area is 60 square metres, what is the length of each of the shorter side ? (a) 10 m (b) 15 m (b) 17 m (d) 5 m
Answer» (d) 5 m Let the length of one side be x m. ∴ Area of the plot = 60 m, length of the other side = \(\frac{60}{x}\) Given, 2\(\big(x+\frac{60}{x}\big) = 34\) ⇒ x² + 60 = 17x ⇒ x² - 17x + 60 = 0 ⇒ x² - 12x - 5x + 60 = 0 ⇒(x - 12)(x - 5) = 0 ⇒ x = 12, 5 ∴ Length of each shorter side = 5 m.

If the perimeter of a rectangular plot is 34 metres and its area is 60 square metres, what is the length of each of the shorter side ? (a) 10 m (b) 15 m (b) 17 m (d) 5 m

Answer»

(d) 5 m

Let the length of one side be x m.

∴ Area of the plot = 60 m, length of the other side = \(\frac{60}{x}\)

Given, 2\(\big(x+\frac{60}{x}\big) = 34\)

⇒ x² + 60 = 17x

⇒ x² - 17x + 60 = 0

⇒ x² - 12x - 5x + 60 = 0

⇒(x - 12)(x - 5) = 0

⇒ x = 12, 5

∴ Length of each shorter side = 5 m.