Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given:
(i) Area : 25a2 – 35a + 12
(ii) Area : 35y2 + 13y – 12
(i) Area: 25a2 – 35a + 12
Since, area is product of length and breadth therefore by factorizing the given area, we can know the length and breadth of rectangle
25a2 – 35a + 12
= 25a2 – 15a – 20a + 12
= 5a (5a – 3) – 4 (5a – 3)
= (5a – 4) (5a – 3)
Possible expression for length = 5a – 4
Possible expression for breadth = 5a – 3
(ii) Area: 35y2 + 13y – 12
35y2 + 13y – 12
= 35y2 – 15y + 28y – 12
= 5y (7y – 3) + 4 (7y – 3)
= (5y + 4) (7y – 3)
Possible expression for length = (5y + 4)
Possible expression for breadth = (7y – 3)