Question

PLEASE HELP!!!!!!!!!!!!!!!!!!!!!
In right triangle ABC, m∠C = 90 and altitude is drawn to hypotenuse . If AD = 4 and DB = 5, find AC.
http://www.castlelearning.com/review/Courses/geometry/MJ19813.gif?v=20010726095750

1. 2r5
2. 5
3. 6
4. r41

* r is the radical sign

Answer 1

One way to do this is to set up 3 equations in 3 unknowns (lengths of AC, DC, and BC).

Equation #1:

(AD)^2 + (DC)^2 = (AC)^2

Equation #2:

(DC)^2 + (DB)^2 = (BC)^2

Equation #3:

(AC)^2 + (BC)^2 = (AB)^2

This is really only 3 unknowns, because we are given the lengths of AD, DB, and AB.

Rewriting and doing a little substitution:

Equation #1:

16 + (DC)^2 = (AC)^2

Equation #2:

(DC)^2 + 25 = (BC)^2

Equation #3:

(AC)^2 + (BC)^2 = 81

Can you do it from here or do you need more help? I can get you the rest of the way if you need it.

Answer 2

yes please

Answer 3

Equation #3 can be re-written: (BC)^2 = 81 - (AC)^2

Equation #2 can be re-written: (DC)^2 = (BC)^2 - 25

So, just looking at these 2 equations, we can substitute #3 into #2:

(DC)^2 = [81 - (AC)^2] - 25 = 56 - (AC)^2

Substituting this expression for (DC)^2 into equation #1 we get:

16 + [56 - (AC)^2] = (AC)^2

72 - (AC)^2 = (AC)^2

72 = 2[(AC)^2]

36 = (AC)^2

AC = 6

Answer 4

thank you so much for all your help!

Answer 5

Good luck to you in all of your studies and thx for the recognition! @christy12345
And you're welcome, this was tough!