Question

In triangle pqr,q is an acute angle,show that square of pr is smaller then squre of pq +square of qr

Answer 1

Solution:

In triangle p qr,→q is an acute angle.

As,we know sum of two sides of triangle is greater than the third side.

p q + q r > p r

Squaring both sides

→→(p q + q r)²> (p r)²

→ (p q )² +  (q r)² +2 (p q). (q r) > (p r)²

Also  , 2 (p q ). (q r)= $\frac{(p q + q r)^2 - (p q- qr)^2}{2}$> p r

→ (p q )² +  (q r)² +A number greater than (p r) > (p r)²

Hence , square of p q +square of qr > square of pr