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 ________ : ________

  • 3
    $\begingroup$ 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

enter image description here

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?

  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.