The ΔPQR is right-angled at P, and PN is an altitude. If QN = 12 in and NR = 6 in, find PN, PQ, PR.

We know that PN^{2} = QN. NR

So, PN = / sqrt{QN. NR}

= / sqrt{12. 6} = / sqrt{72}

PN = 8.5

Now, PNQ is a right angled triangle with PQ as the hypotenuse.

So, PQ^{2} = PN^{2} + NQ^{2}

That means PQ = / sqrt{ PN^{2} + NQ^{2} }

= / sqrt{ 8.5^{2} + 12^{2} }

PQ = 14.7

Same way, PNR is also a right angled triangle with PR as the hypotenuse

So, PR^{2} = PN^{2} + NR^{2}

That means PR = / sqrt{ PN^{2} + NR^{2} }

= / sqrt{ 8.5^{2} + 6^{2} }

PR = 10.4