Determining the height of two overlapping right angled triangles

[ariaaaah]

I am genuinely stuck on how I am supposed to solve this with the given information. This is a practice question for a senior high school competition, and none of my team mates can figure it out.

 

[The Highlander]

View attachment 37701
I am genuinely stuck on how I am supposed to solve this with the given information. This is a practice question for a senior high school competition, and none of my team mates can figure it out.

Just a quick response to bring your question back "in play".
(See here.)

 

[The Highlander]

View attachment 37701
I am genuinely stuck on how I am supposed to solve this with the given information. This is a practice question for a senior high school competition, and none of my team mates can figure it out.

Mark up your diagram as I have done (below), identify similar triangles and use Thales Theorem (Basic Proportionality) to compare the line segments.

The final answer that you should get is that t (XY) ≈ 10.29 cm (or XY = 10\(\displaystyle \frac{2}{7}\) cm)

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Please now come back and show us your attempt (your own drawing & working) to find the answer; if you cannot complete using the suggestions given further help will be offered.

Hope that helps.

 

[lev888]

View attachment 37701
I am genuinely stuck on how I am supposed to solve this with the given information. This is a practice question for a senior high school competition, and none of my team mates can figure it out.

Use similar triangles.