00:01
So i have a rectangle here with some unknown dimensions, and i want to find the dimensions of that rectangle.
00:10
So i know the area formula for a rectangle right here.
00:14
I know that the formula is length times width.
00:17
And i also know the area of this particular rectangle is 120.
00:23
And so i know that whatever i'm multiplying together, it's going to give me 120.
00:27
So i'm going to substitute this in.
00:29
I'm actually going to rewrite the formula of area of a rectangle is length times width.
00:34
And the area of this rectangle is 120 square miles.
00:38
And that's going to equal the length times the width.
00:41
Well, the length, i don't know.
00:43
All it tells me is that it's a rectangle and it has a length.
00:46
But it does tell me that the width is seven miles less than the length.
00:50
So i know that i can write the width in terms of the length as the length minus seven.
00:55
And now i can multiply this out and create an equation.
00:59
That is going to be a quadratic that i can factor.
01:03
So i'm going to keep this 120 here for now, and i'm going to do l times l, which is l squared, and l times minus 7 or negative 7 is negative 7l.
01:13
Now i'm going to subtract 120 from both sides so that all of my terms are on the same side.
01:20
So i have l squared minus 7l minus 120...