Question

draw triangle pqr with sides pq=7cm,qr=8cm and pr=5cm and construct its orthocentre

Answer 1

Here's a geometric explanation. Considering this is the triangle you're trying to construct (provided it exists).

How'd you construct this triangle? You would draw triangle QRS first, which is pretty basic because you know the length of two sides and the included angle. Now, you draw the perpendicular bisector of QS and P is where RS extended meets the bisector.

Except that SR extended on this side of QS will never meet the perpendicular bisector. That's because angle QSP is obtuse.

To understand why, look at this diagram below, where QS' = RS' by construction:

It's easy to see that RS' = 72√≈ 4.94 cm.