 Hello and welcome to the session. In this session we discuss the following question which says, the length and breadth of a park are in the ratio 3 is to 1 and its perimeter is 160 meters, a path 5 meters wide runs inside it along its boundary, find the cost of paving the path at rupees 2 per meter square. Before we move on to the solution, let's recall the formula for the area of rectangle, this is equal to L into B then the formula for the perimeter of rectangle is equal to 2 into L plus p where this L is the length of rectangle and B is the breadth of rectangle. This is the key idea to be used in this question. Let's move on to the solution now. Consider the spark ABCD that is we have ABCD is the park and the shaded portion is the path inside the park. Now that it's given that the length and breadth of a park are in the ratio 3 is to 1 so we take let the length of the park say L is equal to 3 x meters then we also assume the breadth of the park say B is equal to x meters that is AB is equal to 3 x meters and BC is equal to x meters. Now the perimeter of the park would be equal to 2 into L plus p that is 3 x plus x meters this is equal to 2 into 4 x meters equal to 8 x meters is the perimeter of the park as given in the question the perimeter of the park is 160 meters so we say that but the perimeter of the park is equal to 160 meters therefore 160 is equal to 8 x that is x is equal to 160 upon 8 now 8 20 times is 160 so we have x is equal to 20. Now that we have got x equal to 20 so we say the length of the park which we had assumed as 3 x meters would be equal to 3 into 20 meters that is equal to 60 meters then the breadth of the park which we had assumed as x meters would be equal to 20 meters that is we say that L is equal to 60 meters and breadth B is equal to 20 meters so this AB is equal to 60 meters and BC is equal to 20 meters now area of the park ABCD would be equal to 60 into 20 meter square that is equal to 1200 meter square is the area of the park ABCD as given in the question that a park 5 meters wide runs inside the park along its boundary that is we have taken this shaded portion as the park and it is 5 meters wide so let's find out the length of EF this would be equal to AB minus 10 meters since it is 5 meters from both these sides this is also 5 meters and this is also 5 meters so we will subtract 10 meters from AB to get the length of EF so this is equal to 60 meters minus 10 meters equal to 50 meters is EF then next we find out the length of FG this would be equal to BC minus 10 meters as it is 5 meters from both these sides so we subtract 10 meters from BC to get the length of FG that is we have FG is equal to 20 meters minus 10 meters equal to 10 meters so FG is equal to 10 meters now area of EF GH is equal to EF into FG that is equal to 50 into 10 meters square and this would be equal to 500 meters square is the area of EF GH now let's find out the area of the park this would be equal to area of the park ABCD minus area of EF GH now we already have the area of the park ABCD that is equal to 1200 meters square so this is equal to 1200 minus area of EF GH which is 500 meters square so 1200 minus 500 meters square is the area of the park which is equal to 700 meters square in the question we are given that the cost of paving 1 meter square of the park is equal to rupees 2 as given in question so total cost of paving the park is equal to rupees 2 into 700 since 700 meters square is the area of the park so this is equal to rupees 1400 if the total cost of paving the park so rupees 1400 is our final answer this completes the session hope you understood the solution for this question