00:01
This problem says the length of a rectangle is 6 meters less than twice its width.
00:05
The area of the rectangle is 140 meters squared.
00:07
What are the dimensions of the rectangle? so what we are going to do is remember that area of a rectangle can be found from the length times the width of that rectangle, and since we are told the length defined in comparison to the width, what we can do is leave our width as w, but try to define l or our length as something in terms of the width, because we are told that the length is 6 meters less than twice the width.
00:36
Twice the width would be 2 times w, and 6 meters less than that would be minus 6 from that 2w.
00:43
So now that we have another expression that we can use for l, we can use that instead of l to show l times w.
00:51
In this case it will be 2w minus 6 times w, and this is supposed to be equal to our area, which was given as 140 meters squared.
01:00
So now we have an equation that is all in terms of one variable, so we can attempt to solve, and to start solving i will distribute w to 2w and negative 6, which gives us 140 equal to 2w squared minus 6w.
01:14
Now we will subtract 140 over to get our equation equal to zero, so that we can attempt to factor to solve.
01:21
So that is zero equal to 2w squared minus 6w minus 140, and our first step to solve here would be to take out a gcf, so we will have zero equal to the gcf of 2 factored out to leave w squared minus 3w and then minus 70.
01:38
And now to factor our trinomial, we ask ourselves what two numbers would multiply to be our c value negative 70, but add to be the coefficient of our linear term, which is negative 3, and those two numbers would be negative 10 and positive 7, still with our 2 in front equal to zero...