 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that two poles of height 6 meters and 11 meters stand on a plain ground. If the distance between the feet of the poles is 12 meters, find the distance between their tops. We know that Pythagoras theorem states that in a right angle triangle with hypotenuse c and next a and b we have c squared is equal to a squared plus b squared. That is, square of the length of the hypotenuse is equal to sum of squares of length of legs. With this key idea, let us move on to the solution. Now in this question, we are given that two poles of height 6 meters and 11 meters stand on a plain ground. That is, we have two poles ac and bd of height 6 meters and 11 meters respectively. And we are given that distance between the feet of the poles is 12 meters. That is, distance between the feet of the poles a and b is given as 12 meters. And we need to find the distance between the tops. That is, we need to find the distance cd. So, we can say that let ac and bd be two standing poles ac is equal to 6 meters and bd is equal to 11 meters. And distance between the feet of the two poles, that is, a and b is given as 12 meters. And we need to find cd, that is, the distance between their tops. Let cd be equal to x meters. Now from c, we draw a horizontal line which means bd at e. Then we see that ce is equal to ab. As poles are perpendicular to the ground, they are parallel to each other. So, the distance between them remains the same. And therefore we have ce is equal to ab which is equal to 12 meters. As ab is equal to 12 meters, so ce would also be equal to 12 meters. Also we see that ac is equal to be which is equal to 6 meters. And we see that bd can be written as be plus ed. And we know that bd is given as 11, so it would be equal to be, that is, 6 meters plus ed. Which implies that ed would be equal to 11 minus 6, that is, 5 meters. Now here, from the diagram, we see that triangle dec is a right angle triangle where angle e is equal to 90 degrees. So, we say that x, that is, cd is the hypotenuse of the triangle. dec and ce and ed are the two legs of the triangle. And we need to find the distance cd. And from the key idea, we know that Pythagorean theorem states in our right angle triangle with hypotenuse c and legs of the triangle as a and b, we have c square is equal to a square plus b square. So, we apply Pythagorean theorem and we get square of the hypotenuse cd is equal to sum of the squares of the length of legs of the triangle, that is, de square plus ce square. And therefore, we get cd square which is equal to x. So, we have x square is equal to de square and de or ed is equal to 5. So, we have 5 square plus ce square and ce is equal to 12 meters. So, we have 12 square and therefore, we get x square is equal to 5 square, that is, 25 plus 12 square, that is, 144. So, we get the value of x square as 25 plus 144, that is, 169. Which implies that x is equal to square root of 169. Now, taking the positive square root here, we get the value of x as 13. As square root of 169 is equal to square root of 13 into 13, which is equal to 13. So, we say that x is equal to 13, that is, the distance cd is equal to 13 meters. Thus, we can say that distance between the tops of the poles is 13 meters, which is the required answer. This completes our session. Hope you enjoyed this session.