Introduction:
To find the suitable length and breadth of a rectangle with a given area of 35y^2 + 13y - 12, we need to factorize the quadratic expression and then determine the dimensions of the rectangle.

Factorizing the Quadratic Expression:
To factorize the quadratic expression 35y^2 + 13y - 12, we need to find two numbers that multiply together to give -420 (35 x -12) and add up to 13. After some trial and error, we can determine that the numbers are 20 and -21.

Therefore, the quadratic expression can be factorized as (5y + 4)(7y - 3).

Finding the Length and Breadth:
Once we have the factored form of the quadratic expression, we can determine the length and breadth of the rectangle.

Let's assign the factors (5y + 4) and (7y - 3) to the length and breadth, respectively.

Therefore, the length of the rectangle is (5y + 4) and the breadth is (7y - 3).

Summary:
In summary, to find the suitable length and breadth of a rectangle with an area of 35y^2 + 13y - 12, we need to factorize the quadratic expression and assign the factors to the length and breadth. In this case, the length is (5y + 4) and the breadth is (7y - 3).

These are the length and breadth of the rectangle respectively
length=(5y+4)
breadth=(7y-3)