Question

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 1

(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)