The ratio between the length and the breadth of the park is 3: 2. if a man cycling along the boundary of the park at the speed 12 km/hr completes one round in 8 minutes then what is the area of the park(in sq. m).
a. 142000
b. 112800
c. 142500
d. 153600
explain your solution.
solve step by step in the answer !

D is answer.
Perimeter is 2x +3x +2x + 3x = 10x where x is unknown factor of distance.
So P = 10x
Velocity is 12 km/hr = .2 km/min
P =1.6 Km = 10x
x= .16 Km 3x = .48 km, 2x=.32 km
Area = .48 X .32 Km^2
= 153600 m^2

153,600 m^2

From the information given we can make 2 equations:
l=3/2b (l=length, b=breadth) {we know that the ratio of length to breadth is 3:2, meaning that the length is 3/2 longer than the breadth}
2l+2b=p (p=perimeter) {This is from the equation for perimeter of a rectangle}

To use these equations, we need to find the perimeter of the rectangle, which we can do by using the speed and time given here. Looking at the units in the problem we can see that they do not match (hr and min) so we need to do a conversion. The easiest way to convert this is to change minutes into hours, which can be done by dividing by 60.
8min/60=2/15 hours {math simplified here, when I divide by 60 what I am really doing is multiplying by 1 hour and dividing by 60 minutes}

Now that our units match, we can find the perimeter. This can be done by setting the speed equal to some distance over the amount of time it took.
12km/hr= p /(2/15hr)
p=1.6 km

Now that we have the perimeter, we can find the length and breadth. First, it is important to notice that the answer is supposed to be in m, not km, so that can be changed first.
p=1.6km=1600 m { to change from km to m multiply by 1000, because there are 1000 m in a km}

Now I will put this into the second equation giving us 2 equations with the same 2 variables.
l=3/2b
2l+2b=1600

These two can be solved together because the first equation already has l isolated. By taking the value of l from the first equation (3/2b) and substituting it into the second equation b can be found.
2(3/2b)+2b=1600
3b+2b=1600
5b=1600
b=320 m

This can then be substituted back into one of the original 2 equations to find l.
l=3/2(320)
l=480 m

Finally, both of these values can be put into the area equation for a rectangle (area=length*breadth).
480m*320m=153,600 m^2