Question

give a possible expression for the length and breadth of each of the following rectangles in which their areas are given: area=25a^2 - 35a + 12 and area = 35y^2 + 13y +12​

Answer 1

a) 25a² - 35a + 12

The above equation is in the form ax² + bx + c. We have to split the middle term in such a way that it's sum is b i.e. -35 and product is a*c i.e. 25*12.

Now, By Splitting The Middle Term,

→ 25a² - (20 + 15)a + 12

Sum of 20 and 15 is 35 and their product is equal to 25*12.

→ 25a² - 20a - 15a + 12

→ 5a(5a - 4) -3(5a - 4)

→ (5a - 3) (5a - 4)

Therefore, length = (5a - 3) and breadth = (5a - 4)

We will take positive value of a, because negative value of (length and breadth) are not possible.

And for the positive value of a: (5a - 4) < (5a - 3)

b) 35y² + 13y - 12 (correct one)

Solve it by same method (same as above)

→ 35y² + 28y - 15y - 12

→ 7y(5y + 4) -3(5y + 4)

→ (7y - 3) (5y + 4)

Therefore, length = (7y - 3) and breadth = (5y + 4)

Answer 2

Correct Question -

• Give A Possible expression for the length and breadth of each of the following rectangles in which their areas are given:

1. area = 25a^2 - 35a + 12

2. area = 35y^2 + 13y - 12

Factorising the two expressions -

$25 {a}^{2} - 35a + 12 \\ \\ 25 {a}^{2} - 20a \: - 15a + 12 \\ \\ \: 5a(5a - 4) - 3(5a - 4) \\ \\ (5a - 3)(5a - 4)$

So, the length and breadth of the first Rectangle can be (5a - 3 ) and (5a - 4 ) in any order i.e, (5a - 3 ) can be either the length and breadth .

$35 {y}^{2} + 13y - 12 \\ \\ 35 {y}^{2} - 15y + 28y - 12 \\ \\ 5y(7y - 3) + 4(7y - 3) \\ \\ (5y + 4)(7y - 3)$

Similarly here in the second Rectangle , the length and breadth can be (5y + 4 ) and (7y - 3 ) in any order .

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