In triangle ABC, if AC = 17, CB = 10, AD = x, DB = y, AB =21

[little_dragon]

Code: Select all

                  C
                 /|\
              /   | \ 10
       17 /       |  \
      /           |   \
  /               |    \
------------------------
A         x       D  y  B

In triangle ABC, if AC = 17 cm, CB = 10 cm, AD = x cm, DB = y cm, and AB = 21 cm, find the value of x - y.

I have no idea how to get started on this one. It's the last one in the assignment, but it doesn't have a "*" by it, so it shouldn't be this hard!

[DAiv]

Code: Select all

                  C
                 /|\
              /   | \ 10
       17 /       |  \
      /           |   \
  /               |    \
------------------------
A         x       D  y  B

In triangle ABC, if AC = 17 cm, CB = 10 cm, AD = x cm, DB = y cm, and AB = 21 cm, find the value of x - y.

I have no idea how to get started on this one. It's the last one in the assignment, but it doesn't have a "*" by it, so it shouldn't be this hard!

If you label side CD as z, you can use Pythagoras' Theorem to form equations for each small triangle, ACD and BCD. If you then equate them so z disappears, you'll end up with an equation in x² and y².

You've also been given AB = 21 = x + y, so now you have two unknowns and two equations.


DAiv

[little_dragon]

So I get x^2 + z^2 = 17^2 and y^2 + z^2 = 10^2, so z^2 = 17^2 - x^2 and z^2 = 10^2 - y^2. This makes 17^2 - x^2 = 10^2 - y^2, so 289 - 100 = x^2 - y^2.

They gave me that x + y = 21. I used x^2 - y^2 = (x + y)(x - y) to get (21)(x - y) = 189, so x - y = 9.

Is it okay that I didn't find numbers for x or y? Thanks.

[stapel_eliz]

Is it okay that I didn't find numbers for x or y?

Since they didn't ask you to find the values of x and y, and since you found the value that they did ask you to find, your answer should be fine!

Eliz.