 Hello friends welcome again to this problem-solving session on triangles. I know triangles is one topic which gives a lot of nightmares to 10 graders, but never mind I have a belief that if you practice enough ample number of questions and This would be sorted out. So in that pursuit we are uploading a lot of solved examples the procedure should be you should See the question and pause the video try to solve it and If you're not able to solve then definitely go and see how we are approaching this problem in solving And after that you must have a couple of lines as of as a as a learning as to what did you learn in this? question and if at all you made a mistake that also should be highlighted and Whenever you try and whenever you solve problems, you must have a log book Basically where you have you know mentioned all the steps don't try to scribble on a piece of paper and Lose that sheet because every question you practice should become a good learning for you So let's start and solve this question in this question. It is given that de is parallel to BC and clearly ABC is a triangle and AD is given to be equal to X and DB is X minus 2 so this length is X minus 2 And AE is X plus 2. So this is X plus 2 from here to here and EC is X minus 1 Okay, and you have to find X Now the moment you see such kind of a problem and a diagram Many questions would not have diagrams also So hence you have to draw it properly and once you you have the diagram in front of you And when you see things like AD parallel to BC in a triangle, the first thing which would come in your mind is Thales theorem or basic proportionality theorem. So by basic basic proportionality or functionality Theorem which is also called Thales theorem. So I'll write Thales theorem Thales theorem, we know that in a triangle if DE is parallel to BC then AD upon DB is equal to AE upon EC Is it it? AE upon EC so hence We should be very clear as to what all All Values are given so hence Now everything is in terms of X so we can definitely write what we can write X upon X minus 2 will be equal to and AE is how much X plus 2 and What about EC? EC is X minus 1. So this is the equation. Just check ED upon DB, sorry AD upon DB is equal to AE upon EC and that's what we wrote here and now it's simple Rearrangement and solving so hence if you see it is X times X minus 1 cross multiplying is equal to X plus 2 and X minus 2 Isn't it? So solving what will you get? You open the bracket. You'll get X square minus X is equal to X square minus 2x plus 2x and minus 4 Isn't it? Actually, it is you know, you shouldn't you should have noticed is something what X square minus 2 square, which is These two terms this gets cancelled. Yep, whichever way so this is nothing but X square minus X is equal to X square minus 4. So obviously X square X square will go So X equals to 4 Easy, is it it right? So what is the learning? Learning is please remember What is basic proportionality theorem or Thales theorem? So there is theorem just to recap those who have not Understood it or let's say if you don't remember it. So if I have a triangle ABC ABC Such that E DE is parallel to DE is parallel to BC now these arrow signs depict that both these lines are parallel Then we say that AD upon DB is equal to AE upon EC. This is what? basic proportionality theorem or Thales theorem say and we use the same result To find the solution in this given question, right? So hence Idea is you must know Thales theorem and you must be able to apply it correctly in a given situation