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What is the value of x?

 

 Mar 16, 2021
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since PQ and JL are parallel, we can determine that triangles KJL and KPQ are similar. 

 

now, we can use the similar triangle ratios to help us find x:

 

\(\frac{x-6}{x-6+3} = \frac{x-6}{x-3}\)

 

and we also have

\(\frac{x}{x+5}\)

 

we know that these two equal each other. so we get an equation:

 

\(\frac{x-6}{x-3}= \frac{x}{x+5}\)

 

let's cross multiply, and then continue simplifying -

 

\((x-6)(x+5) = (x-3)x\)

\(x^2-x-30 = x^2-3x\)

\(2x = 30\)

\(x=15\), which is option D

 

as you can see, the equation ended up simplifying quite nicely!

 

hope this helped! please let me know if you are still confused :)

 Mar 16, 2021

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