 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that from the given triangle ABC find EC, we know that side splitting theorem states that a line parallel to a side of a triangle that intersects the other two sides in distinct points divides those two sides proportionally. That is in triangle PQR DE is parallel to QR then PD upon DQ is equal to PE upon ER. With this key idea we shall proceed to the solution. Here we are given triangle ABC in which DE is parallel to BC, AD is given as 7, DB is given as 14, AC is given as 24 and AE as X and we have to find EC. Here we should see that AE plus EC is equal to AC that is X plus EC is equal to 24 which implies that EC is equal to 24 minus X so to find EC we will find the value of X. Now using side splitting theorem here in triangle ABC we have DE is parallel to BC then AD upon DB should be equal to AE upon EC. Now substituting the values of AD, DB, AE and EC here we get 7 upon 14 is equal to X upon EC that is 24 minus X. This implies that 1 by 2 is equal to X upon 24 minus X. Now on cross multiplying we get 24 minus X is equal to 2 into X that is 2X which further implies that 24 is equal to X plus 2X which implies that 24 is equal to 3X. Now dividing both sides by 3 we get 24 by 3 that is 8 is equal to 3X upon 3 that is X or we can write it as X is equal to 8 so AE which is equal to X is equal to 8 and EC that is equal to 24 minus X will be equal to 24 minus 8 that is equal to 16 so EC is equal to 16 which is the required answer. This completes our session hope you enjoyed this session.