In the triangle, PQ = QR, PR = 15 cm and angle PQR = 90°. Calculate PQ. Answer PQ = ... cm

1. Set up Pythagoras' theorem using the equal sides

Let $PQ=QR=x$ cm.

Since ngle PQR=90^\circ, $PR$ is the hypotenuse.

$x^2+x^2=15^2$

2. Solve for the equal side length

$2x^2=225$
$x^2=112.5$
$x=\sqrt{112.5}=10.606\ldots$

So, to 3 significant figures, $PQ=10.6$ cm.