Question

Question 6
Angles Q and R of a $\Delta$PQR are ${25}^{\circ }$ and ${65}^{\circ }$.
Write which of the following is true:
(i) $P{Q}^2+Q{R}^2=R{P}^2$
(ii) $P{Q}^2+R{P}^2=Q{R}^2$
(iii) $R{P}^2+Q{R}^2=P{Q}^2$

Answer 1

In $\Delta PQR$,
$\Rightarrow {25}^{\circ }+{65}^{\circ }+\angle RPQ=180$ [By Angle sum property of a $\Delta$]
$\Rightarrow {90}^{\circ }+\angle RPQ={180}^{\circ }\Rightarrow \angle RPQ={180}^{\circ }-{90}^{\circ }={90}^{\circ }$
Thus, $\Delta PQR$ is a right angled triangle, right angled at P.
$\therefore (Hypotenuse{)}^2=(Base{)}^2+(Perpendicular{)}^2$
[By Pythagoras theorem]
$\Rightarrow (QR{)}^2=(PR{)}^2+(QP{)}^2$
Hence, Option (ii) is correct.