Question

what is the length of a rectangle if the area is $x^2 + 3x - 4$ and the width is $(x - 1)$?
a. $(x + 4)$
b. $(x - 4)$
c. $(x - 3)$
d. $(x + 3)$

Explanation:

Step1: Recall area formula for rectangle

The area of a rectangle is $A = l \times w$, where $l$ is length, $w$ is width. Rearranged, $l = \frac{A}{w}$.

Step2: Substitute given expressions

Substitute $A = x^2 + 3x - 4$ and $w = x-1$:
$l = \frac{x^2 + 3x - 4}{x-1}$

Step3: Factor the quadratic numerator

Factor $x^2 + 3x - 4$: find two numbers that multiply to $-4$ and add to $3$, which are $4$ and $-1$.
$x^2 + 3x - 4 = (x+4)(x-1)$

Step4: Simplify the rational expression

Cancel the common factor $(x-1)$:
$l = \frac{(x+4)(x-1)}{x-1} = x+4$

Answer:

A. $(x + 4)$