Question

Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given: Area: $35y^2+13y-12$.

Answer 1

Step 1: List the Formula and Conditions

We know that the area of a rectangle with length $l$ and breadth $b$ is given by,

Area $a=l\times b....................\left(1\right)$

The given expression is $35y^2+13y-12$ which is a quadratic equation.

We know that a quadratic equation has two factors in the form of linear equations.

If $a=35y^2+13y-12$

Step 2: Factorize the equation

Upon factorizing the equation we get,

$a=35y^2-15y+28y-12$

$=5y\left(7y-3\right)+4\left(7y-3\right)$

$=\left(7y-3\right)\left(5y+4\right)$

Comparing it with equation $\left(1\right)$ we get,

Length $l=7y-3$ and breadth $b=5y+4$

Hence, the expressions for the length and breadth of the rectangle is $7y-3$ and $5y+4$.