 Hello friends, let's work out the following problem. It says that triangle A,B,C be similar to triangle D,E,F and their areas be respectively 64 cm2 and 121 cm2. If E,F is 15.4 cm, find B,C. Now before moving on to the solution, let us understand the theorem which will be helping us to solve this problem. Now the theorem says, area of triangle A,B,C on area of triangle D,E, the ratio of the squares of the corresponding sides that is A,B square upon is equal to E,F square is equal to C,A square upon F,B square. Let's now proceed on with the solution. We are given that triangle A,B,C is similar to triangle D,E given to us the area of triangle A,B,C is given cm2 and the area of triangle 121 cm2 and we are given that the length of the side E,F is 15.4 cm and we have to find the length of the side B,C. The length of the side B,C using by the key idea ratio of the areas of the two triangles, area of triangle A,B,C upon area of triangle D,E,F is equal to the ratio of the square of the corresponding sides and here we have to find the length of the side B,C. So here we need to take this, so area of triangle A,B,C upon area of triangle D,E,F is equal to B,C square upon E,F substitute the values given to us area of triangle A,B,C is 64 cm2 area of triangle D,E,F is 121 cm2 we have to find B,C we have to take the square of B,C square is equal to 15.64 can be written as 8 square and 121 can be written as 11 square. Now taking square root on both sides we have is equal to 15.4 into 8 upon 11 length of side B,C as 11.2 cm, this completes the question session, bye for now take care have a nice day.