 Hello friends, welcome to another session on problem solving in the topic triangles. The given question says that triangle AD in this given figure triangle ADE is equal to angle B. So while I am reading the question, I'll also mark it for you all to understand. So ADE is equal to angle B. We have to show that triangle ADE ADE is similar to ABC. So this is triangle ADE is similar to triangle ABC. Okay, first is this and then it's given that AD is equal to 3.8 centimeter. So this length is 3.8 centimeter here. BE is 2.1 centimeter. BC is 4.2 centimeter. Okay, and we have to find out BE. Let's say this is X and we have to find this X out here. Okay, so how to approach this problem? Clearly, the first one is to prove ADE is ABC. So we know three criteria triple A, double A and SAS. So let's see which one fits in here. So I will write given angle ADE is equal to angle B. Okay, and also given is one thing which I missed is this is 90 degrees also. This is also given irrespective of that. It will be similar. So triangles would be similar. We'll see how. So also given is angle C is equal to 90 degrees. Okay, now so in triangle ABC and triangle ADE, you can see the vertices have been written in that order such that the correspondence is established. What do I mean? I mean that angle A is angle A and B is D corresponding to D and C is corresponding to E and why is that? Let's check. Clearly in both these triangles, angle A is common. Angle A is equal to angle A. This angle is common to both the triangles which I have mentioned. Also, angle, it's given that angle ADE is equal to angle B. So one angle each or two angles are equal in the two given triangles. Therefore, we can conclude triangle AED or ABC first. Let's say ABC is similar to triangle A and corresponding to B is D. So ADE are similar. These two triangles are similar by what? By AA, similarity criterion, similarity criterion. So when they are similar, then we can go for equality of the ratios of the sides. Therefore, what can we say? We can say that first of all, what is given? EB is given. EB. So this length is given. So the full EA is not given. And we have to find out X. So how to go about this? AE is also given. Sorry, I missed on this. So this is 3.6 centimeters. AE is given. ADE is given. So which I have mentioned. BE is 2.1 given and BC is 4.2 given. So we have to find out DE. Correct? It should not be a big deal now. So how to go about it? So first, let's write the similarity. So angle ABC is similar to triangle A and corresponding to B is D. So ADE. So that means if I have to find out ED. So here is ED. So let's write ED. This we have to find out. DE. And corresponding to DE is simply BC. So let's write BC here. And then we just need to know one more side. So AB. So we know AB. So let's write AB here. So BC by AB and AD. So corresponding to AB is AD. So let's write AD here. So what I have done is I have just taken corresponding sides by these arrow marks. You can identify which one is corresponding to which side. So BC clearly is equal to DE upon AD into AB. Isn't it? So what is DE guys? DE. So that's what we have to find out. So hence let's write instead of writing like this. Let's write DE. Let's write DE. So DE is equal to directly I can say BC upon AB into AD. Okay, what is BC? BC is 4.2. What is AB guys? If you see AB is nothing but 2.1 plus 3.6. Isn't it? 2.1 plus 3.6. And here into AD. AD is 3.8. And the result will be in centimeters. Okay, so let's solve this. So what is this? 4.2 divided by 5.7 into 3.8 centimeters. So this goes by 2 and this goes 3. 19 times 2 is 38. 19 times 3 is 57. And this is simply 14. So 1.4 into 2 is 2.8 centimeters. So we could establish the length of X and this is equal to 2.8 centimeters. This is how you have to solve. So first we establish the similarity and then use the property of two similar triangles that the corresponding sides ratios are equal. And hence we could find out the value of X.