Corresponding triangles with sides and angles

Question

Assume that triangle ABC ~A'B'C' with angles A and A' corresponding, angles B and B' corresponding, and angles C and C' corresponding. Find the indicated missing parts.

 

If AB=1.0, BC=2.0, AC=4.0, and the shortest side of triangle A'B'C' is 6.0, find the other two sides of triangle A'B'C'.

Answer 1

Because the triangles are similar, they will be proportionate. Since the shortest side of the first triangle is 1 (length AB) and that similar side is 6 in the new triangle, the new triangle is 6 times the size of the similar triangle. Therefore, side AB = 6, side BC = 12, and side AC = 24

Answer 2

Jeffrey's answer is correct! You can also use proportions (ratios) to solve this. Since the two shortest sides correspond, you could do 1/6 = 2/x to find the medium side and 1/6 = 4/x to find the large side. Just cross multiply and solve for x! :)