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You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

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Guillotine

Weekly Problem 9 - 2006
What fraction of the area of the rectangle is shaded?

Two Right Angles

Stage: 3 and 4 Short Challenge Level: Challenge Level:1



In the figure above, $PQ=2\frac{1}{3}$, $PS = 6\frac{6}{7}$, $PQR$ and $PRS$ are right-angled triangles, and the angles $QPR$ and $RPS$ are the same.

How long is $PR$?

 

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.

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