Two Right Angles
Weekly Problem 4 - 2008
In the figure given in the problem, calculate the length of an edge.
In the figure given in the problem, calculate the length of an edge.
Age
14 to 16
Challenge level
Problem
Image
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.
Student Solutions
Triangles $QPR$ and $RPS$ are similar. So:$\frac{PR}{PS}=\frac{PQ}{PR}$. Hence $PR^2=PQ\times PS=\frac{7}{3}\times\frac{48}{7}=16$.
So $PR$ is $4$ units long.