 Hello all and welcome to the session. Today the question is on a map drawn to a scale of 1 is to 20,000 a triangular plot PQR of land has the following measurement. PQ is equal to 4 centimeters, QR is equal to 5.5 centimeters at angle PQR is equal to 90 degrees. Calculate first part the actual length of the side QR in kilometers, second part the actual area of the plot in square kilometers. Now, before starting the solution of the question, we should know some results. That is, if a model of a map is drawn to a scale of 1 is to P, then the scale factor K is equal to 1 over P. And length of the model of map is equal to K times length of the actual figure. Also, area of the model of map is equal to K times area of the actual figure. Now, this will work as a key idea for solving out this question. And now we will start with the solution. Now it is given that the map is drawn to a scale of 1 is to 20,000. This means the scale factor K will be equal to 1 over 20,000. Now, in the first part we have to find the actual length of side QR in kilometers. And it is given that the length of the side QR on the map is equal to 5.5 centimeters. Now using the formula, which is given in the key idea, length of the model on a map is equal to K times length of the actual figure. So, we will write length of the side QR on map is equal to K times actual length of the side QR. Now the length of the side QR is 5.5 centimeters, putting the value of K, which is 1 over 20,000 into actual length of the side QR. Now this implies of side QR is equal to 5.5 into 20,000. Further, which is equal to 1,10,000 centimeters. Now changing in kilometers, it will be 1.5 into 20,000. Therefore, length of side QR is equal to 1.1 kilometers. And now in the second part, we have to find the actual area of the plot in square kilometers. Now for the second part, area of triangle PQR. Now here, PQR is given as a right angle triangle. So the area of this triangle will be equal to half base into height, which is equal to half RQ into PQ. Which is equal to 1 over 2 into RQ is 5.5 centimeters and PQ is 4 centimeters. Now here, 2 into 2 is 4. So this will be equal to 11 centimeters square. Now according to the formula, which is given in the key idea, area of the model on a map is equal to K times area of the actual figure. So therefore, we can write area of the triangle on a map is equal to K square times area of the actual triangle. This implies area of the triangle on the map is 11 centimeters square. So 11 centimeters square is equal to 120,000 square into area of the actual triangle. This implies 11 centimeters square is equal to 120,000 into 120,000 into area of actual triangle. Now this implies area of actual triangle is equal to 20,000 into 20,000 into 11 centimeters square. Now changing the centimeters square, it will be 20,000 into 20,000 into 11 over 100 into 100 into 1000 into 1000 centimeters square. Now these three zeros will be cancelled with three zeros here. These three zeros will be cancelled with the three zeros here. One zero will be cancelled with one zero here and one zero will be cancelled with one zero here. So this will give 2 into 2 into 11 that is 44 over 100 kilometers square. This is equal to 0.44 kilometers square. Therefore, the actual length of side qr in kilometers is equal to 1.1 kilometers. And the actual area of triangle plot in square kilometers is equal to 0.44 kilometers square. So this is the solution of the given question and that's all for this session. Hope you all have enjoyed this session.