Length of the median of the trapezoid is 10 in the median...

Transcript

00:03 All right.

00:05 So we're given a trapezoid, and we're told that that mid -segment is 10 inches long.

00:12 We know the ratio of the areas of the two parts is three to five.

00:16 So the ratio of the areas of the top to bottom, three to five.

00:21 All right, and we want to find the length of the shorter base.

00:24 All right, well, let's think about this.

00:26 We know about the ratio of the area.

00:28 So let's think about what would this area actually look like.

00:31 So i'm just going to call this guy x right now.

00:33 Maybe call it b1 and b2, but i'm going to call it x and y just because i'm looking for one of those two values in there.

00:40 All right.

00:42 So let's go ahead and set up our area formulas for this.

00:46 So i know the area of a trapezoid is one half the sum of the bases.

00:51 So for the top one, the bases would be whatever x is plus 10, all right, and then times the height.

00:58 And i don't know what the height is, but since it's the mid -segment, i know it's the same height.

01:02 In both.

01:02 So i'm just going to make the height equal to one and not even worry about it.

01:06 You can put the h in there if you want, and when we set up our fraction, it's going to cancel out.

01:11 Maybe that's a better way to think about it rather than just assuming it's a certain thing.

01:15 So the area of the top trapezoid would look like this.

01:19 Now, i know what the ratio of those two areas is, is three to five.

01:24 So i'm going to go ahead and set up my ratio right now.

01:26 So let's find the area of the bottom trapezoid.

01:29 Well, that's going to be one half.

01:31 And for that one, it's going to be one, it's going to going to be 10 plus y.

01:34 That's the two trapezoids or sorry, the two bases of the trapezoid there.

01:40 And then again, times whatever that h value is.

01:42 You can kind of see why it doesn't really matter.

01:44 I'm just going to end up canceling them out.

01:46 I know that these two things are in the ratio of three to five...

length of the median of the trapezoid is 10 in.. The median divides the trapezoid into two areas whose ratio in 3:5. The length of the shorter base is: