Question

What is the length, in units, of segment CD?

Answer 1

@Calcmathlete

Answer 2

ALright. You see, <ACD = <BAC
This means that all of the corresponding angles are congruent to each other in the triangles. THis proves them similar.
Use the Pythagorean theorem to find side BC
49 = 25 + b^2
b^2 = 24
BC = 2√6
Now let's find a ratio. 2√6/7 is the ratio. Then, find the hypotenuse using a proportion.
2√6/7 = 7/x
2x√6 = 49
x = 49/2√6
x = 49√6/12

Answer 3

so I got 10, is that right?

Answer 4

Is it multiple choice?

Answer 5

yes, but 10 is not one my options

Answer 6

my options are 6, 7, 8.5, or 9.8..

Answer 7

this is why I needed help, because I had also gotten 10 before posting the question, and realized 10 wasnt any of my options

Answer 8

It's 9.8. This is because you can use the ratio of the other side.
5/7 = 7/x
5x = 49
x = 9.8
It's confusing because they didn't specify which way it is similar.

Answer 9

oh ok, I see! Thanx so much!! yea I figured...I already put 9.8 anyways because it was the closest to 10! thank you!

Answer 10

Actually, you can tell because the angles have to be congruent to their repective order. Therefore, it would tell you which legs were similar.

Answer 11

thank you ;)