Question

the area of a rectangular rug is given by the trinomial ( r^2 - 4r - 77 ). what are the possible dimensions of the rug? use factoring.
the length and the width of the rectangle are (square).
(use a comma to separate answers as needed.)

Explanation:

Step1: Factor the quadratic trinomial

We need two numbers that multiply to $-77$ and add to $-4$. These numbers are $-11$ and $7$.
$r^2 - 4r - 77 = (r - 11)(r + 7)$

Step2: Identify rectangle dimensions

The area of a rectangle is length $\times$ width, so the factored terms represent the dimensions.

Answer:

$r - 11$, $r + 7$