Question

15. Give possible expressions for the length and breadth of each of the following
rectangles, in which their areas are given:
Area : 25a2 – 35a + 12
Area : 35y2 + 13y-12​

Answer 1

Solution :

( i ) Area = 25a² - 35a + 12

Area = Length × Breadth

The possible expression for length and breadth would be the factors of Area

Area = 25a² - 35a + 12

Splitting the middle term

= 25a² - 20a - 15a + 12

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

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

• Length = ( 5a - 3 ) units
• Breadth = ( 5a - 4 ) units

( ii ) Area = 35y² + 13y - 12

Splitting the middle term

= 35y² + 28y - 15y - 12

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

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

• Length = ( 7y - 3 ) units
• Breadth = ( 5y - 4 ) units

Answer 2

Step-by-step explanation:

By getting factors we can determine possible expressions for the length and breadth:

1. 25a^2 – 35a + 12= (5a - 4) * (5a - 3)

Length= 5a - 3  and breadth = 5a - 4

2. 35y^2 + 13y-12​= (7y -3) * (5y + 4)

Length= 5y + 4  and breadth =7y -3