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How to find other length of the base on a Trinagle?

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Hi, I was confused on with this triangle.

At first I thought I should've started off with Pythagoras' Therom

I got the **square root of (x**^{2}+180) = c

After I got c, I didn't know if it mattered.

I tried getting the smaller triangle's hypotenuse, which is the **square root of (4 + x**^{2}) = 2 + x

After that, I made the 2 hypotenuses equal to equal other

2 + x = square root of (x^{2 }+ 180)

4 + x^{2} = x^{2 }+ 180

Yeah.. I got lost here since I will be losing x...

Can someone give me a tip or explain? :) Thanks

Re: How to find other length of the base on a Trinagle?

Quote:

Originally Posted by

**Chaim**

$\displaystyle \frac{x+12}{6}=\frac{x}{2}$

Re: How to find other length of the base on a Trinagle?

side lengths of similar triangles are proportional ...

$\displaystyle \frac{6}{12+x} = \frac{2}{x}$