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Let the sides of the rectangle be x and y meters respectively. Then 2x + 2y = 48 2 (x+y) = 48 x+y = 24 y = 24 -x

We have, xy = 135 So, x (24 – x) = 135 24x – x^{2} = 135 x^{2} -24x + 135 = 0 x^{2} – 9x – 15x + 135 = 0 (x-9) (x -15) = 0 x = 9 m or 15 m So, when x = 9m, y = 24 – 9 = 15m And when x = 15, y = 24 -15 = 9 m So, the sides of rectangle are 15m and 9m.

5) The roots of the equation (x + 3) (x – 3) = 160 are

Let the speed of the car is x km/hr. Then Speed = distance/ time:

=2

=>

x^{2} – 5x – 750 = 0 x^{2} – 30x + 25x – 750 = 0 (x – 30) (x + 25) = 0 x =30 or x = -25 The negative value of x is inadmissible; therefore the speed of the car is 30 km/hr.