Question

A rectangular plot has dimensions in the ratio 3:2. If a woman running along the circumference of the plot at a speed of 12 km/hr completes one round in 480 seconds, then the area of the plot (in sq. m) is:

Answer 1

Time =480sec =480/60 min=8min.

8min=8/60=0.13hours

distance=speed×time
distance=12×0.13km
=1.56km
=1560m

This is also the perimeter of rectangular plot.

Let the ratio multiplyier of sides is x.

so length=3x and width=2x.

so....


2(3x+2x)=10x=1560

10x=1560

x=156.

The area of plot=length×width

=(3x)(2x)
=6x^2
=6(156^2)
=6×24336
=146026m^2

Answer 2

L:b = 3:2

circumference(d) = 2 (l+b) = 2(3x+2x)

= 2*5x = 10x

s = d/t

s = 12 * 5/18

= 30/9 m/sec

t = 480 sec

s=d/t

30/9 = 10x /480

30/9 = x/48

x = 30*48 /9

x = 160

l = 3*160 = 480 m

b = 2*160 = 320 m

Area of the plot = l*b = 480*320 = 153600 sq m