00:01
So here we have a rectangle.
00:04
We are given that the area of this rectangle is 105 feet squared.
00:14
We are also given that the length of this rectangle is one foot less than the width.
00:20
So let's denote the width as n and the length as n minus one.
00:30
We know that the area is defined as length times width.
00:40
So using our definitions of length and width here, we have the area as equivalent to n minus 1 times n.
00:50
So plugging in what we already know for the area, we have 105 equals n minus 1.
01:01
Times n.
01:04
Now we can expand this equation to get 105 equals n squared minus n.
01:19
We will now move this 105 to the other side to get n squared minus n minus 105 equals zero.
01:31
To solve for n, we will have to use the quadratic equation.
01:36
I will remind you of the quadratic equation.
01:40
X equals negative b plus or minus b squared minus 4 ac square root over 2a.
01:56
So we will now solve this equation using the quadratic formula and we get n is equal to one plus or minus negative one squared which was one minus four times one times negative 105 square root over two times two times two times now, these will cancel to make this a plus sign...