Maths-
General
Easy
Question
In triangle PQR, RT= 9 cm, PT=16 cm, altitude QT=12 cm, Prove that ∠PQR=90o.
Hint:
Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.
If a is the perpendicular, b is the base, and c is the hypotenuse, then according to the definition, the Pythagoras Theorem formula is given as
c2= a2 + b2
The correct answer is: Hence, it is proved that ∠PQR is a right angle.
Applying Pythagoras theorem in △QTR
QR2 = QT2 + RT2
QR2 = 122 + 92
QR2 = 225
Applying Pythagoras theorem in △QTP
QP2 = QT2 + PT2
QP2 = 122 + 162
QP2 = 400
Applying Pythagoras theorem in △PQR
PR2 = QP2 + QR2
9+16)2 = 400 + 225
625 = 625
So, LHS = RHS
So, △PQR is a right-angled triangle with right angle at Q
Final Answer:
Hence, it is proved that ∠PQR is a right angle.
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