1 00:00:02,176 --> 00:00:05,076 >> So here's a word problem involving a rectangle. 2 00:00:05,596 --> 00:00:09,976 We know that the perimeter of a rectangle is 100 yards, and we want to find 3 00:00:09,976 --> 00:00:16,236 out what the dimensions of that rectangle are if the length if 20 yards more than the width. 4 00:00:16,946 --> 00:00:20,076 So, let's see, perimeter, what does that mean? 5 00:00:20,186 --> 00:00:23,866 Well, perimeter is just the distance you would walk 6 00:00:23,866 --> 00:00:26,356 if you walked all the way around that rectangle. 7 00:00:27,306 --> 00:00:32,976 So we could write down perimeter equals distance around the shape. 8 00:00:32,976 --> 00:00:36,226 And this is true not just for rectangle but for other shapes as well. 9 00:00:37,086 --> 00:00:39,276 So let's see what we've got here. 10 00:00:39,496 --> 00:00:44,526 Let's draw a rectangle and go ahead and label its dimensions. 11 00:00:44,526 --> 00:00:47,636 And when they say dimensions they mean length and width. 12 00:00:48,226 --> 00:00:55,216 So let's call that length L, and let's call the width W. And then on my picture here I can draw 13 00:00:55,216 --> 00:00:57,786 in the lengths and draw in the widths. 14 00:00:58,656 --> 00:01:01,036 So let's think about this. 15 00:01:01,036 --> 00:01:03,826 We know the perimeter, and I'll call it P, 16 00:01:04,346 --> 00:01:07,736 is equal to what you get if you add up all the sides. 17 00:01:08,456 --> 00:01:19,666 So in this case that would be L plus W plus L plus W. And if we simplify the right hand side 18 00:01:19,666 --> 00:01:24,896 of that equation we get P equals 2L plus 2W. 19 00:01:24,896 --> 00:01:29,166 And this is a formula that you can use anytime you're dealing with the perimeter 20 00:01:29,166 --> 00:01:32,816 of a rectangle, P equals 2 lengths plus 2 widths. 21 00:01:33,526 --> 00:01:36,396 So now let's see how this applies to this problem. 22 00:01:36,966 --> 00:01:42,346 Well, we know that the length is 20 yards more than the width. 23 00:01:43,706 --> 00:01:47,516 So really if we knew what the width was we could figure out the length. 24 00:01:47,516 --> 00:01:48,616 It wouldn't be too bad. 25 00:01:49,116 --> 00:01:55,356 So I'm going to go back and erase those Ls and change them to -- well, let's see. 26 00:01:55,436 --> 00:02:01,776 The length is 20 yards more than the width, so how about W plus 20 for the length. 27 00:02:02,336 --> 00:02:04,826 So that other wide is W plus 20 as well. 28 00:02:05,726 --> 00:02:12,496 So the width is called W and the length is now called W plus 20 because of the relationship 29 00:02:12,496 --> 00:02:13,836 that we're given in this problem. 30 00:02:14,576 --> 00:02:19,866 Okay, so let's go ahead and see how we can put that into our equation. 31 00:02:20,646 --> 00:02:26,436 We've got 100 for the perimeter that was given in the problem equals 2 times, 32 00:02:26,436 --> 00:02:29,826 now instead of L I'm going to put W plus 20. 33 00:02:31,006 --> 00:02:34,996 And then don't forget your plus 2W at the end. 34 00:02:35,146 --> 00:02:37,626 So now it's just a matter of solving a linear equation. 35 00:02:37,626 --> 00:02:38,856 This shouldn't be too bad. 36 00:02:38,856 --> 00:02:45,466 On the right hand side I'm going to go ahead and distribute my 2 so I get 2W plus 40. 37 00:02:46,226 --> 00:02:48,616 Do not lose that plus 2W at the end. 38 00:02:48,616 --> 00:02:49,486 It's important. 39 00:02:50,496 --> 00:02:51,686 I'm still simplifying. 40 00:02:51,686 --> 00:02:54,256 On that right hand side I have like terms. 41 00:02:54,256 --> 00:03:01,486 So I'm going to go ahead and combine the 2W and the 2W to get 4W plus 40. 42 00:03:02,696 --> 00:03:07,766 So now let's see, at this point I can't simplify either side any further. 43 00:03:08,136 --> 00:03:11,296 So I'm going to go ahead and subtract 40 from each side. 44 00:03:11,716 --> 00:03:14,926 That will leave me with 60 equals 4W. 45 00:03:15,836 --> 00:03:20,776 And if I want to get that W by itself it is attached to the 4 by multiplication. 46 00:03:20,826 --> 00:03:25,216 So I'm going to divide both sides by 4 and I get 15 for W. 47 00:03:26,386 --> 00:03:31,506 So what this means is the width of that rectangle is 15 yards. 48 00:03:32,516 --> 00:03:37,816 And now if the width is 15 let's see what that means for the length. 49 00:03:37,816 --> 00:03:42,766 Well, if we put 15 for the W and then we add 20 we get 35. 50 00:03:43,676 --> 00:03:48,246 So the length is going to be 35 yards. 51 00:03:48,866 --> 00:03:49,656 And that's it.