Question

Give possible expressions for the length and breadth of the rectangle whose area is given by $24x^2-15x$.

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 $24x^2-15x$ which is a quadratic equation.

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

If $a=24x^2-15x$

Step 2: Factorize the equation

Upon factorizing the equation we get,

$a=24x^2-15x$

$=3x\left(8x-5\right)$

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

Length $l=3x$ and breadth $b=8x-5$

Hence, the expressions for the length and breadth of the rectangle is $3x$ and $8x-5$.