**Q.15.** Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given:^{ }

(i) Area: 25a^{2} - 35a + 12 (ii) Area: 35 y^{2} + 13y - 12

**Solution:**

Since, area is product of length and breadth therefore by factorizing the given area, we can know the length and breadth of rectangle.

(i) Area: 25a^{2} - 35a + 12

We can write, 25a^{2} - 35a + 12 = 25a^{2} - 15a -20a + 12

= 5a(5a - 3) - 4(5a - 3)

= (5a - 4)(5a - 3)

Hence, possible expression for length = 5a - 3

And possible expression for breadth = 5a - 4

(ii) Area: 35 y^{2} + 13y - 12

We can write, 35 y^{2} + 13y - 12 = 35y^{2} - 15y + 28y - 12

= 5y(7y - 3) + 4(7y - 3)

= (5y + 4)(7y - 3)

Hence, possible expression for length = 5y + 4

And possible expression for breadth = 7y - 3