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https://gyazo.com/66f47546602b91315cceecd66927c129

In triangle PQR, X is a point on PQ. RX is perpendicular to PQ. Work out the ratio PX : XQ. Give your answer in its simplest form.







Answer ________ : ________

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    $\begingroup$ What is the problem you are facing in the problem? Any thoughts? $\endgroup$ – Matti P. Dec 7 '18 at 7:54
  • $\begingroup$ It would be better if you showed your work too, including where and why you’re stuck. $\endgroup$ – KM101 Dec 7 '18 at 7:58
  • $\begingroup$ Thank you for replying and sorry for not providing enough information. I simply don't get the question, when it says to work out the ratio of PX : XQ, I just don't get what I am supposed to do. I know what a ratio is but I am confused over what to do. Thank you for understanding $\endgroup$ – THELichCA Dec 7 '18 at 8:08
  • $\begingroup$ You need to use the Pythagorean Theorem to calculate the length of the sides $\overline{PX}$ and $\overline{XQ}$. Then, you can find the ratio of their sides by $\frac{\overline{PX}}{\overline{XQ}}$. $\endgroup$ – KM101 Dec 7 '18 at 8:11
  • $\begingroup$ So the ratio will simply be: "The length of PX : The length of XQ"? $\endgroup$ – THELichCA Dec 7 '18 at 8:13
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Note that $\triangle PXR, \triangle QXR$ are right angled at $X$. Use the pythagorean theorem in both triangles:

$PX^2+RX^2=PX^2+16^2=PR^2=20^2\implies PX=\sqrt{20^2-16^2}$

$QX^2+RX^2=QX^2+16^2=QR^2=34^2\implies QX=\sqrt{34^2-16^2}$

Can you now work out the ratio $PX:QX=\frac{PX}{QX}$ in simplest terms?

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  • $\begingroup$ The ratio would be 12:30 = 6:15 = 2:3 $\endgroup$ – THELichCA Dec 7 '18 at 8:19
  • $\begingroup$ Yes, that's correct. $12:30::2:5$ $\endgroup$ – Shubham Johri Dec 7 '18 at 8:20
  • $\begingroup$ You simplified the ratio incorrectly. $6:15 \implies 2:5$. Other than that, it’s correct. $\endgroup$ – KM101 Dec 7 '18 at 8:22

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