Question

15. Give posible expressions for the length and breadth of each of the following
rectangles in which their areas are given.
Area: (i) 35y² + 13-12
(ii) 25a²-35a+12​

Answer 1

Answer:

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

(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)

Step-by-step explanation:

hope my answer help you

Answer 2

Step-by-step explanation:

Area : 35y

2

+13y−12

Area of rectangle - Length×Breadth

35y

2

+28y−15y

35y

2

+28y−15y

7y(5y+4)−3(5y+4)

(7y−3)(5y+4)

∴ Length =(7y−3)

Breadth =(5y+4)