>> Here's another word problem, it's a geometry word problem,
where we're going to look at a picture of a rectangle.
We're going to use the information on the rectangle and the fact
that its area is 54 square feet, to find the length and width.
So it looks like the length is x plus 2 and the width is x minus 1,
and the area of a rectangle is length times width.
That's the area for a rectangle, or you could say length times width equals area.
All right so looking at our picture, I'm going to do the second one.
The length times the width is the area, so the length,
x plus 2 times the width, which is x minus 1 is 54.
Now it's really, this is a certain number of feet, this is a certain number
of feet, and the area is square feet.
We'll fill in the correct units later.
All right, so what do we have here?
I need to simplify the left hand side.
It's factored, but the right hand side does not equal 0, so it's not helpful
to be factored unless one side equals 0.
So we need to multiply this out using the foil method or any other method you might use,
x squared minus x plus 2 x minus 2 equals 54, and combining like terms here,
I have x squared plus x, and then I need to subtract 54 on this side, on both sides,
so that it is set equal to 0, so I get x squared plus x minus 56 is equal to 0.
Ok, so now we have a quadratic trinomial, so we factor, again this is the easier ones to factor
because we just have a nice x squared, how convenient, factors of 56,
that have a difference of 1 the middle terms are going to be 8 and 7,
and I need to have a plus 8 and a minus 7.
Now remember these aren't your answers, 8 and -7,
you have to solve by writing x plus 8 equals 0, or x minus7 equal 0.
You set each factor that has a variable equal to 0, so x can be -8, or x can be 7.
Well, look at our picture here, if x was -8, this side would be -9,
well you can't have a negative side, it's not that x can't be -8,
if this would have been some, something else, like 1 minus x, that would have worked,
cause you'd have 1 minus -8, which is a positive 9, it's because when you plug in a -8,
that side doesn't make any sense, you can't have x be -8, and have this picture make sense.
Ok, what if x was7?
Well, if you put in 7 for x, you'd have 7 minus 1
and you'd have 7 plus 2, well that seems to work out ok.
So let's do that.
x looks, looks like x could be 7, so this would be 7 minus 1, and this would be 7 plus 2,
so this length would be 6, and this length would be 9.
Hey, all right, we wanted the area to be 54 square feet.
Well 6 times 9 is 54.
So therefore, you did it.
The length is 9 feet, the width is 7 feet, and that's the answer to this one.