Question

Given the same triangle from part C, if line segment AB measures 12 inches and line segment BC measures 5 inches what is the measure of line segment BD? Show and explain your work.

Answer 1

4.615 in

Explanation:

Triangle ABC and ABD are similar because they have two corresponding congruent triangles that is right angle and ∠A. Triangle ABC and BCD are similar because they have two corresponding congruent triangles that is right angle and ∠C. Therefore Triangle ABC, ABD and BCD are similar. Since they are similar, then their sides are proportional in length.

In triangle ABC, using Pythagoras theorem:

AC² = AB² + BC²

AC² = 12² + 5²

AC² = 144 + 25 = 169

AC² = 169

AC = √169 = 13 in

Using similar triangle for ΔABC and ΔABD:

`(AC)/(AB)= (BC)/(BD) \\\\(13)/(12)=(5)/(BD)\\\\BD=(12*5)/(13)\\ BD=4.615\ in`