In ΔPQR, PQ = 17 in, PR = 10 in, QR = 21 in. Find the altitude from P to the side QR

To get the altitude we proceed as follows:
Half perimeter of the triangle is:
s=(17+10+21)/2
s=24
Area of the triangle will be:
A=√s(s-PR)(s-PQ)(s-QR)
A=√(24×7×3×14)
A=84

But:
A=1/2*base*height
hence:
84=1/2×21×h
⇒h=(2×84)/21=8