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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 ________ : ________

THELichCA
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    What is the problem you are facing in the problem? Any thoughts? – Matti P. Dec 07 '18 at 07:54
  • It would be better if you showed your work too, including where and why you’re stuck. – KM101 Dec 07 '18 at 07:58
  • 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 – THELichCA Dec 07 '18 at 08:08
  • 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 $\frac{\overline{PX}}{\overline{XQ}}$. – KM101 Dec 07 '18 at 08:11
  • So the ratio will simply be: "The length of PX : The length of XQ"? – THELichCA Dec 07 '18 at 08:13
  • Yes, that’s what it’ll be. – KM101 Dec 07 '18 at 08:15
  • You have to cancel the common factors from the numerator and denominator. If you get the answer as $4:12$, you have to cancel $4$ and report the answer as $1:3$ – Shubham Johri Dec 07 '18 at 08:16
  • Thank you very much for your answers! – THELichCA Dec 07 '18 at 08:16

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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?

Shubham Johri
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