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

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