The area of a rectangular rug is given by the trinomial r squared minus 4 r minus 77r2−4r−77. what are the possible dimensions of the rug? use factoring.

Step-by-step explanation:

The area of the rectangular rug is given by this equation:

The area must be a number greater than 0 since a negative area, or an area equal to 0 wouldn't have much sense. So:

Let's find the roots of this equation using the quadratic formula:

Now, let's evaluate the area for for example r=1.05:

The result is greater than zero, so for the values make sense.

Now let's evaluate the area for for example r=0.5 and r=-0.7:

The result is less than zero, so for the values don't make sense.

Now, let's evaluate the area for for example r=-1:

The result is greater than zero, so for the values make sense

However, since negative values of r wouldn't make much sense (I never heard about of -8 inches for example) the possible dimensions of the rug are just: