Question

please solve fast..........,......

Answer 1

Since we can consider any triangle with Q as acute angle, so let us consider right-angled triangle PQR with ∠Q acute<90°.

Also, ∠p = 90° = right angle and QR is the hypotenuse of ΔPQR.

Therefore, using Pythagoras theorem, we can write

\begin{lgathered}PR^2+PQ^2=QR^2\\\\\Rightarrow PR^2+PQ^2+PQ^2=QR^2+PQ^2\\\\\Rightarrow PR^2+2PQ^2=QR^2+PQ^2.\end{lgathered}
PR
2
+PQ
2
=QR
2

⇒PR
2
+PQ
2
+PQ
2
=QR
2
+PQ
2

⇒PR
2
+2PQ
2
=QR
2
+PQ
2
.
​


Since PQ²>0, so PR²<PQ²+QR².

Hence showed.