# Pythagoras theorem and ratio question

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 ________ : ________

• What is the problem you are facing in the problem? Any thoughts? – Matti P. Dec 7 '18 at 7:54
• It would be better if you showed your work too, including where and why you’re stuck. – KM101 Dec 7 '18 at 7:58
• 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 7 '18 at 8:08
• 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 7 '18 at 8:11
• So the ratio will simply be: "The length of PX : The length of XQ"? – THELichCA Dec 7 '18 at 8:13

## 1 Answer 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?

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