Question

determine the expression for the width of a rectangle
the area, $a$, of a rectangle is $120x^{2}+78x - 90$, and the length, $l$, of the rectangle is $12x + 15$. which of the following gives the width, $w$, of the rectangle?
$10x - 19$ $10x - 6$ $9x + 4$ $8x - 6$

Explanation:

Step1: Usar fórmula de área de rectángulo

Sabemos que $A = l\times w$, entonces $w=\frac{A}{l}$. Dado que $A = 120x^{2}+78x - 90$ y $l=12x + 15$.

Step2: Factorizar el numerador y el denominador

Factorizamos $A = 120x^{2}+78x - 90=6(20x^{2}+13x - 15)=6(5x - 3)(4x+5)$. Factorizamos $l = 12x + 15 = 3(4x + 5)$.

Step3: Simplificar la fracción

$w=\frac{6(5x - 3)(4x+5)}{3(4x + 5)} = 2(5x - 3)=10x-6$.

Answer:

$10x - 6$