# 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

**Solution:**

i) Area of rectangle = 25a² - 35a + 12

But we know that, Area of rectangle = length × breadth

Hence, we shall factorise the given expression 25a² - 35a + 12

Now taking 25a² - 35a + 12, find two numbers p, q such that:

- p + q = co-efficient of a
- pq = product of the co-efficient of a² and the constant

p + q = - 35 (co-efficient of a)

pq = 25 × 12 = 300 (product of the co-efficient of a² and the constant term.)

By trial and error method, we get p = -20, q = -15.

Now splitting the middle term of the given polynomial,

25a² - 35a + 12 = 25a² - 20a - 15a + 12

= 25a² - 15a - 20a + 12

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

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

∴ 25a² - 35a + 12 = (5a - 4)(5a - 3)

Thus, Length = 5a - 3, Breadth = 5a - 4

(OR) Length = 5a - 4, Breadth = 5a - 3

ii) Area of rectangle = 35y² + 13y - 12

But we know that, Area of rectangle = length × breadth

Hence, we shall factorise the given expression 35y² + 13y - 12

Now taking 35y² + 13y - 12, find two numbers p, q such that:

- p + q = co-efficient of y
- pq = product of the co-efficient of y² and the constant

p + q = 13 (co-efficient of y)

pq = 35 × (- 12) = - 420 (product of the co-efficient of y² and the constant term.)

By trial and error method, we get p = 28, q = -15.

Now splitting the middle term of the given polynomial,

35y² + 13y - 12

= 35y² + 28y - 15y - 12

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

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

∴ 35y² + 13y - 12 = (5y + 4)(7y -3)

Hence, Length = 5y + 4, Breadth = 7y - 3

(OR) Length = 7y - 3, Breadth = 5y + 4

**Video Solution:**

## 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

### NCERT Solutions Class 9 Maths - Chapter 2 Exercise 2.5 Question 15:

**Summary:**

The possible expressions for the length and breadth of each of the following rectangles, in which their areas are given 25a² − 35a + 12 and 35y² + 13y − 12 are Length = (5a − 4), Breadth = (5a − 3) (OR) Length = (5a − 3), Breadth = (5a − 4) and Length = (5y + 4), Breadth = (7y − 3) (OR) Length = (7y - 3), Breadth = (5y + 4) respectively.