 Hello and welcome to the session. In this session we discussed the following question which says, the area of a rhombus is equal to the area of a triangle whose base and the corresponding altitude are 10 centimeter and 12 centimeter respectively. If one of the diagonals of the rhombus is 6 centimeters, find the length of the other diagonal. Before we move on to the solution, we will recall the formula for the area of a triangle and area of a rhombus. Area of a triangle is equal to half into b into h where this b is the base of the triangle and h is the altitude of the triangle. Then we have the area of a rhombus is equal to half into d1 into d2 where d1 d2 are the lengths of the two diagonals of a rhombus. This is the key idea to be used in this question. Let's move on to the solution now. In the question we are given that the base of triangle is 10 centimeters and its altitude is 12 centimeters that is base of the triangle say b is 10 centimeters then altitude of the triangle that is h is equal to 12 centimeters. So now area of the triangle would be equal to half into b into h that is equal to half into 10 into 12 centimeters square now 2 6 times is 12 so this is equal to 60 centimeters square is the area of the triangle. Now length of one diagonal of the rhombus say d1 is given as 6 centimeters that is we have d1 is equal to 6 centimeters and we take let the length of the other diagonal of the rhombus be equal to d2 then the area of the rhombus is equal to half into d1 into d2 that is equal to half into 6 into d2 centimeters square is the area of the rhombus now 2 3 times is 6 so this is equal to 3 d2 centimeters square is the area of the rhombus. Now according to the question we have that the area of the triangle is equal to the area of the rhombus so therefore 60 is equal to 3 d2 this means d2 is equal to 60 upon 3 20 times is 60 therefore we get d2 is equal to 20 centimeters thus the length of the other diagonal of the rhombus is equal to 20 centimeters so 20 centimeters is our final answer this completes the session hope you have understood the solution for this question