 Hello and welcome to another session on triangles. We have taken another question The question says the perimeters of two similar triangles are 30 centimeter and 20 centimeter respectively If one side of the first triangle is 12 centimeter, you have to mind the corresponding side of the second triangle. So we will start with drawing a Triangle, so let's say this is one triangle and let's draw a similar triangle to this triangle So I'm going to select this one and copy Paste and then stretch it. Yep. So this looks like similar triangle To the given triangle. Let me just reduce share. Yeah, so this is there are two similar triangles Let's say this triangle's name is a b c a D C and this one let it be D e f Okay. Now It's given that Perimeters of the two triangles so the bigger one is 30 centimeters. So this is 30 centimeter and The 20 centimeter respectively. So this one is the the second one a b c is let's say, so I'm writing here perimeter of Triangle a b c is the smaller of the two, right? So 20 centimeter What does this mean? This means that a b plus b c plus C a Is equal to 20 centimeter Clear then secondly I can say D e plus E f Plus fd is how much 30 centimeter Perimeter is nothing but some of the three sides of the triangle. Okay now We have to find out If one of the sides of the first triangle so in this case the first triangle corresponds to 30 centimeter perimeter triangle So D e let's say this is D e. So let's say D e is 12 centimeter First triangle was was the triangle with higher perimeter. So D is 12 centimeter. So we have to find out corresponding sides of a b c triangle so we have to find out a b okay so let's Try and find the solution. So always you remember you have to remember that what was given given is Triangle a b c is Similar to triangle D e f is it it is given? So what would this mean? So let me write it here. So this will mean this will mean that a b by D e is equal to bc by E f Is equal to C a by fd Correct. These are the three Equal ratios because these are triangles are similar. So can I not equate it to let's say k all of them Let them let me say this these ratios are equal to a value k because all of them are same So if I compare these two Can I not say that a b is equal to k times D e Similarly, the other ones can be written as bc is equal to k times E f and C a is equal to k times E f. Sorry c fd correct now let's Go back to this these equations. So what can I say I can say I Can say let me yeah, so let me write it here now So a b plus bc plus c a can I not replace a b by k d e bc by k e f and c by k fd Yes, I can so I can write k d e plus k e f Plus k fd. These are the three sides and this is equal to 20 centimeter Is it and now if I can take k common you will get d e plus e f plus fd This is equal to 20 and we already know d e plus e f plus fd is given to be equal to 30. So k into 30 Is equal to 20. So what do I get k is 2 by 3? Correct k is 2 by 3 the moment we know k but k is 2 by 3. Let's Find out the value of a b so a b upon a b upon d e already we have established that is k a b upon d e if you if you see this one this one here a b upon d e Is equal to k. So what was k value k is value was 2 by 3 So what will be a b a b will be simply 2 upon 3 Into d e isn't it? I'm sorry. This doesn't look like d here. So let me correct it. This is d D e right. So what is a b clearly 2 by 3 into d e which is 12 centimeter? So this is nothing but 8 centimeter. So using similarity we could find out The value of a b in this case which comes out to be 8 centimeter. Okay, so let's solve Few more problems of this type