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# similar triangles

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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