00:01
We have triangle a, b, c is the right triangle, with a being the right angle, and we're told that line segment a, d is perpendicular to c b at point d.
00:16
So let's just go ahead and make that little right angle symbol help us.
00:21
So we have some theorems that are going to help us figure this out.
00:24
We're trying to find the area of triangle adb.
00:28
We have an altitude drawn.
00:33
So we can use the theorem that says if we have an altitude drawn from the right angle of any right triangle, then the two triangles form, that's this one and this one, are similar to the original triangle, and all three triangles are similar to each other.
00:49
All we need is triangle abc.
00:54
They're similar by angle, angle, similarity.
00:58
Similarity.
01:00
It's triangle that's called triangle d -a -b so we can get our corresponding sides in the right spot.
01:08
So those were similar.
01:12
Now we need some corresponding sides.
01:17
What do we have in triangle d -a -b? where we have this hypotenuse is 12.
01:24
So we need the hypotenuse of the large triangle and use the pythagorean theorem.
01:29
To do that.
01:30
So c .b, we need to know the measure of cb, cb, i'll put in parentheses squared, is equal to the 16 squared plus 12 squared.
01:42
And when we square those, add those together, and take the square root, we get the measure of cb is 20.
01:49
So cb equals 20 units.
01:53
And we're doing all that just so we can get the scale factor.
01:56
Now we have triangle a, b, c, c, the big triangle, if we put it over the smaller triangle, triangle dab, we can say that the scale factor is that 20 over 12...