Writing equations to represent geometric problems | Grade 8 (TX TEKS) | Khan Academy

We're told the perimeter of the rectangle shown is 17x units. The area of the rectangle is 15x square units. Write an equation that represents the perimeter, and also write an equation that represents the area.

So pause this video and see if you can write those two equations.

All right, now let's do this together. So let's tackle this first one. Write an equation that represents the perimeter. The perimeter is going to be the length of all of the sides. So you have this side right over here which is 4x + 2, and then you're going to add this side over here, which is 2 and a half, plus this side over here which is going to be 4x + 2 again. So, plus 4x + 2, plus this side which is going to be 2 and A2 plus 2 and a half. Well, that's going to be equal to the perimeter, which they told us is 17x units. So that is going to be equal to 17x.

And we're done! That's all they wanted; they just want us to write an equation that represents the perimeter. We don't have to solve it.

So now let's do the same thing for the area. The area of a rectangle is going to be our base times our height, or our height times our base. So we could say it's 2 and A2 * (4x + 2). Then, that's going to be our area, which they say is 15x² units. So that's equal to 15x. We could have also written it the other way; we could have said that the area, which is 15x, is equal to 2 and A2, the height, times (4x + 2).

So, a lot of different ways to approach it, but in both cases, we are now done.