Question

Please leave an explanation for how to do this, I edited the question so I can't cheat with the answer.

Triangle Q T S is shown. Angle A T S is a right angle. An altitude is drawn from point T to point R on side Q S to form a right angle. The length of T S is 4 x, the length of Q R is 5, and the length of R S is 11.
What is the length of side TS?

Answer 1

So wht do you need help wit

Answer 2

Bit confused, any chance you can post a picture of the triangle that's shown? Not sure where R came from if the triangle is QTS

Answer 3

I cant help you out if I cant see the picture

Answer 4

I drew it out based on the information given

Answer 5

But first let's go back to the basics

So when we have two right triangles like this

there's this formula

so for the triangle I'm attaching

\(\sf \dfrac{BC}{AC} = \dfrac{AC}{DC}\)

and

\(\sf \dfrac{BC}{AB} = \dfrac{AB}{DB}\)

and

\(\sf \dfrac{DC}{AD} = \dfrac{AD}{DB}\)

Answer 6

@AZ I see a "Angle ATS", is that a misspelling or something? I don't see it in your drawing

Answer 7

So from my image, the one you would need to use is

\(\sf \dfrac{BC}{AB} = \dfrac{AB}{DB}\)


So can you apply that formula to your question and solve for x?

Answer 8

And remember that the question is asking for the length of TS, so that means you have to plug back x into 4x to get your final answer

Answer 9

\(\color{#0cbb34}{\text{Originally Posted by}}\) @typicalfoxgirl
@AZ I see a "Angle ATS", is that a misspelling or something? I don't see it in your drawing
\(\color{#0cbb34}{\text{End of Quote}}\)

Good catch. I assumed that said QTS and that's the only thing that would make sense. I forgot to put the right angle for it so here's an updated drawing

Answer 10

\(\color{#0cbb34}{\text{Originally Posted by}}\) @AZ
\(\color{#0cbb34}{\text{Originally Posted by}}\) @typicalfoxgirl
@AZ I see a "Angle ATS", is that a misspelling or something? I don't see it in your drawing
\(\color{#0cbb34}{\text{End of Quote}}\)

Good catch. I assumed that said QTS and that's the only thing that would make sense. I forgot to put the right angle for it so here's an updated drawing
Created with RaphaëlReply Using Drawing
\(\color{#0cbb34}{\text{End of Quote}}\)
Thanks for the assistance!

Answer 11

You're welcome!

Let me know what you get and I can check it for you :)