Video Transcript

Hello my name is Whitney and this video explains how to find dimension using quadratic equations. So this is just one example of the different types of word problems you may encounter when studying quadratic equations. Here we have a rectangle with an area, a width, and a height represented by a,w, and h. And we have several equations to describe these values. The first is that the area of our rectangle is equal to 24 square feet. Another equation that I have, already written on the board, is that the width of our rectangle is equal to 8 feet plus 2 times our height. So w is equal to 2h plus 8. Now, what we need to do is write an equation that will be able to incorporate both of these different equations that we already have written on the board. And a way we can do that is to define what our area is equal to. Not only is it equal to 24, but it's also equal to the width times the height. Since we have the width written in terms of height, we can take that w equation and plug it in here. When we rewrite this we have h x 2h plus 8=24. When we distribute this we'll see that we're going to have a quadratic equation. 2h squared plus 8h, bring the 24 over, minus 24, is equal to 0. So now we're going to use the unfoil method which is just to write the quadratic as the product of 2 separate parenthesis. Since we have a minus sign here, our signs will be different. Which we're not sure of the order so we'll just guess this order first. Since we have a 2h squared here we're going to put a 2h and h. And we have to think of a way how to get 24 multiplying 2 numbers together that add to give us 8. We also have to consider this 2 here. So lets think, We have 24 and 1. That wont work for us. 8 and 3, probably wont work for us either. We could try 4 and 6 and see if that works. So we say 4 and 6. If we multiply 2 by either of these will the sum or difference give us 8? What we see if we multiply the 2 by the 6 we'll get 12 minus the 4, since the minus sign's out here, that'll give us a value of 8. So now what we can do is solve these two sets of parenthesis. We have 2h-4. Then h 6. So we want to find the value of h for both of these. For this one we're going to move the 4 over and divide by 2. And we say that h is equal to positive 2. For the second equation h, when we multiply 6 on both sides, I'm sorry, when we subtract 6 on both sides, will give us minus 6. Now since our word problem is dealing with dimensions we know that we can never have a negative dimension and so the value of our h is 2 and we we have an expression for what w is equal to, 2h 8. We plug in the 2 here and we get 2x2=4 plus 8 will give us 12. So the dimensions of our equation are equal to w by h, which we can write as a 12 by 2. Thanks for watching, this video explains how to use quadratic equations to solve for dimensions.