# 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.

## 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.