Question

the area of a rectangle is given by the expression: 21x² - 19xy - 12y² and the width is 7x + 3y. find the length of the rectangle:

Explanation:

Step1: Recall the formula for the area of a rectangle

The area of a rectangle \(A = \text{length}\times\text{width}\). Let \(l\) be the length and \(w = 7x + 3y\), \(A=21x^{2}-19xy - 12y^{2}\). Then \(l=\frac{A}{w}=\frac{21x^{2}-19xy - 12y^{2}}{7x + 3y}\).

Step2: Factor the numerator

We factor \(21x^{2}-19xy - 12y^{2}\).

$$
LATEXBLOCK0
$$

Step3: Simplify the fraction

Since \(l=\frac{(3x - 4y)(7x + 3y)}{7x + 3y}\), cancel out the common factor \((7x + 3y)\) (assuming \(7x+3y
eq0\)).

Answer:

\(3x - 4y\)