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
We have to find a number whose sum = -35 and product =25×12=300
We get -15 and -20 as the numbers
[-15 + -20 = -35 and -15 × -20 = 300]
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
Using the splitting the middle term method,
We have to find a number whose sum = 13 and product = 35 × -12 = 420
We get -15 and 28 as the numbers
[-15 + 28 = 13 and -15 × 28 = 420]
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)