Question

15. Give possible expressions for the length and breadth of each of the following
rectangles, in which their areas are given:
Area : 25a - 35a +12
Area: 35y2 + 13-12
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Answer 1

Problem based on geometrical figure:

First we determine all the factors of the given polynomial by splitting middle term and then consider any of the factor as any of the dimension.

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Solution:

 

(i) Area : 25a² – 35a + 12

 

Since, area is product of length & breadth therefore by factorizing the given area by middle term splitting, we can know the length and breadth of rectangle.

25a² – 35a + 12

 

[ Middle term splitting]

= 25a²-15a -20a + 12

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

= (5a – 4)(5a – 3)

Hence,possible expression for length = 5a – 4

Possible expression for breadth = 5a – 3

 

(ii) Area :35 y²+13y- 12

35 y² + 13y – 12

 

[By middle term splitting]

= 35y²-15y+28y -12

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

= (5y + 4)(7y – 3)

 

Hence,possible expression for length = (5y + 4)

Possible expression for breadth = (7y – 3)

 

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Hope this will help you....