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CBSE Class 9 Mathematics Question 29 of 30

Polynomials — Question 15

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15
Question

Question 15

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) 25a2 - 35a + 12

Area of Rectangle = Length x Breadth

= 25a2 - 35a + 12

= 25a2 -(20a + 15a) + 12

= 25a2 -20a -15a + 12

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

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

Hence, one possible answer is : Length = 5a - 3, Breadth = 5a - 4

(ii) 35y2 + 13y - 12

Area of Rectangle = Length x Breadth

= 35y2 + 13y - 12

= 35y2 +(28y - 15y) - 12

= 35y2 + 28y - 15y - 12

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

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

Hence, one possible answer is : Length = 7y - 3, Breadth = 5y + 4