 Hi and welcome to the session. I am Asha and I am going to help you solve the following problem which says give possible expressions for the length and breadth of each of the following rectangles in which their areas are given. So as we know the area of a rectangle is equal to length into breadth. So what we will do in this problem is try to reduce 25a square minus 35a plus 12 and 35y square plus 13y minus 12 as the product of two binomials such that one is the length and another one is the breadth. So this is the key idea. We are going to use in this problem to find the possible length and breadth. Let us now start with the solution and the first one is area is equal to 25a square minus 35a plus 12 which can further be written as 25a square minus 35 can be written as 15 plus 20 into a plus 12 which we have written by splitting the middle term to 20 is equal to the product of 25 into 12 also 15 plus 20 is equal to 35. Now opening the brackets we have 25a square minus 15a minus 20a plus 12. Now taking 5 a common from the first two terms and minus 4 common from the next two terms it can further be written as 5a into 5a minus 3 left in the bracket now taking minus 4 common we have 5a minus 3 in the bracket. Now taking 5a minus 3 common it can be written as 5a minus 3 into 5a minus 4 and thus the area is equal to 5a minus 3 into 5a minus 4. And now as we know area of rectangle is equal to length into breadth so one of these two binomials is length and another one is breadth so one possible answer is equal to 5a minus 3 breadth equal to 5a minus 4. So this completes the first part and now proceeding on to the second part where area is equal to 35y square plus 13y minus 12. Now this can further be written as 35y square plus 13 can be written as 28 minus 15 into y minus 12. Now opening the brackets we have 35y square plus 28y minus 15y minus 12. Now taking 7y common from the first two terms and minus 3 common from the last two terms this can further be written as 7y into 55 plus 4 minus 3 into 5y plus 4. And now taking 55 plus 4 common this can further be written as 55 plus 4 into 7y minus 3. And thus area is equal to 55 plus 4 into 7y minus 3 and since area is equal to the length into breadth so any one of this can be the length and another one is the breadth so a possible answer is equal to 7y minus 3 breadth is equal to 55 plus 4. So this completes the solution hope you enjoyed this session take care and have a good day.