Pythagoras theorem and ratio question

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.

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Answer ________ : ________

Answer 1

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?