Right Triangle Proportions

Question

Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AD=4 and BD=2, what is the length of DC?

Answer 1

ABC, ADB and ACD are all right triangles

which all have the same ratio of similar sides

AD:DB = DB:CD

4/2 = 2/CD cross multiply

4CD = 2x2 = 4

CD =4/4 = 1

Answer 2

Hi Anika,

First, draw a right triangle Δ ABC

second , draw altitude from B ( B = 90) and its name is BD

Third, you have 2 segments on the hypotenuse AD and DC that AD = 4 and you need to find DC

Forth, there is a property in any right triangle that BD² = AD * DC

Fifth, BD = 2 AD = 4 replace to the property -------> 2² = 4 * DC ------> DC = 1

I hope it is useful,

Minoo

Answer 3

Hello Anika!

I would suggest drawing the triangle, so you can follow my line of thought. By drawing, you'll see the triangle ABD is also a right triangle. Using the Pythagoras's Theorem, you can find:

AB = 2√5

Note that ABD and ABC are similar. So:

AB/AC = AD/AB

AB² = AC*AD

20 = AC*4

AC = 5

AC = AD + DC

5 = 4 +DC

DC = 1

Fell free to message with more doubts!