If bc=5.3, cd=8.8, and ad= 14.3, find ab to the nearest tenth.

The picture above shows us that triangle ABC and triangle ACD are similar triangles by showing us that then have congruent angles. This tells us that each side of the triangle is bigger/smaller than the other triangle by the same factor. To find this out, we use two corresponding sides of the two triangles. In this case, two corresponding lengths that are given to us are BC and CD. If we divide CD by BC, this tell us that triangle ACD is approximately 5/3 bigger than triangle ABC. Using this, we can figure out the length of AB. We simply take 14.3 and divide it by 5/3. We divide because we are trying to mind the magnitude of the length of the smaller triangle. If we were looking for the length of the larger triangle, we would have multiplied. After dividing 14.2 by 5/3, we find that the length of AB is about 8.6.