 Hello, and welcome to the session. In this session, we'll discuss a question which says that the area of the triangle with what it says 6 minus 3, 3k, and minus 7, 7, is 15 square units. Find the value of k. Now, before starting the solution of this question, we should know what is out. And that is, in a triangle A, B, C with A, X1, Y1, B, X2, Y2, and C, X3, Y3, the area of the triangle A, B, C is given by the formula which is 1, Y2 into X1 into Y2 minus Y3, the whole plus X2 into Y3 minus Y1 the whole plus X3 into Y1 minus Y2 the whole. Now, this result will work out as a key idea for solving out this question. Now, we will start with the solution. Given the vertices of the triangle 6 minus 3, 3k minus 7, 7. Also, the area of the triangle is equal to 15 square units. Now, let 6 minus 3 as X1, Y1, 3k as X2, Y2, and minus 7, 7 as X3, Y3. Now, using this formula which is given in the key idea, here the triangle will be equal to 1 by 2 into into k minus 7 the whole plus 3 into 7 minus of minus 3 the whole plus into minus 3 minus k the whole which is further equal to 1 by 2 into on solving this we get 6 square minus 42 plus 21 plus 9 plus 21 plus 7 the whole which is further equal to 1 by 2 into and on solving this we get 13k plus 9 the whole. Therefore, the triangle is equal to 1 by 2 into 13k plus 9 the whole. Now, we have the area of the triangle as 15 square units. So, putting this value here this implies 15 is equal to 1 by 2 into 13k plus 9 the whole which further implies 30 is equal to 13k plus 9. Which implies 30 minus 9 is equal to 13k which implies 21 is equal to 13k which further implies 13k is equal to 21 and which gives k is equal to 21 by 13. So, the value of k is equal to 21 by 13. So, this is the solution of the given question and that's all for this session. Hope you all have enjoyed the session.