Give possible expressions for the length and breadth of each of the fo

1.	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
Answer» (i) Area: 25a² – 35a + 12 = 25a² – 20a – 15a + 12 = 5a(5a – 4) – 3(5a – 4) = (5a -4) (5a – 3) length × breadth = Area of rectangle (5a – 4) (5a – 3) = 25a² – 35a + 12 ∴ Length = (5a – 4) Breadth = (5a – 3) (ii) Area : 35y² + 13y – 12 Area of Rectangle – Length × Breadth 35y² + 13y – 12 35y² + 28y – 15y 7y(5y + 4) – 3(5y + 4) (7y – 3) (5y + 4) ∴ Length = (7y – 3) Breadth = (5y + 4)

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

Answer»

(i) Area: 25a² – 35a + 12

= 25a² – 20a – 15a + 12

= 5a(5a – 4) – 3(5a – 4)

= (5a -4) (5a – 3)

length × breadth

= Area of rectangle (5a – 4)

(5a – 3) = 25a² – 35a + 12

∴ Length = (5a – 4)

Breadth = (5a – 3)

(ii) Area : 35y² + 13y – 12

Area of Rectangle – Length × Breadth 35y² + 13y – 12

35y² + 28y – 15y

7y(5y + 4) – 3(5y + 4)

(7y – 3) (5y + 4)

∴ Length = (7y – 3)

Breadth = (5y + 4)