Find the shorter leg of right triangle ABC.

Question

Right triangle ABC is similar to right triangle DEF, which is a 3-4-5 triangle. If the hypotenuse of right triangle ABC is the square root of 5, find the shorter leg of right triangle ABC.

Answer 1

First, draw your triangles.  Because they are similar, the corresponding angles are congruent, but the corresponding sides are unequal.

 

Let AB = shortest leg                DE ∼ AB

Let BC = medium leg                EF ∼ BC

Let AC = hypotenuse                DF ∼ AC

 

Similar shapes allow us to set a proportion of the sides. 

 

Ratio of shortest leg = ratio of hypotenuse

 

AB / DE = AC / DF

 

 

Plug in the given values from the problem.

 

AB / 3 = √(5) / 5

 

 

AB = 3 * (√(5) / 5)