Television Transition

Stage: 3 and 4 Short Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
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The ratio width : height of television screens is changing from the traditional $4:3$ to the widescreen $16:9$.

If a traditional screen and a widescreen have the same area,
then what is the ratio widescreen width : traditional width ?
 
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.  

This problem is taken from the UKMT Mathematical Challenges.