Question

in the figure pq=24cm. qr=26cm angle par =90°, pa =6cm and ar =8cm . find angle qpr

Answer 1

triangle par is a right angled triangle right angled at a
therefore pr^2 = pa^2 + ar^2 by pythagoras theoram
pr^2 = 36 + 64
pr ^2 = 100
pr = 10
now in triangle pqr, pq^2 + pr^2 = 576 + 100 = 676
also qr^2 = 26^2 = 676
therefore pq^2 + pr^2 = qr^2
therefore by converse of pythagoras theoram
angle p or angle qpr = 90

Answer 2

Answer:

PYTHAGORAS THEOREM: In a right angle triangle the square of the hypotenuse is equal to the sum of the square of the other two sides.

CONVERSE OF PYTHAGORAS THEOREM: In a triangle if square of one side is equal to the sum of the squares of the other two sides then the angle opposite to first side is a right angle.

SOLUTION:

Given :

PQ = 24cm  ,QR = 26cm,  ∠ PAR = 90°,  PA = 6cm and AR  = 8cm

In ∆ PAR,

PR² = AR² + AP²

[By Pythagoras theorem]

PR² = 8² + 6²

PR² = 64 +36

PR² = 100

PR = √100

PR = 10 cm

In ∆ QPR

QR² = QP² + PR²

26² = 24² + 10²

26² = 576 + 100

26² = 676

676 = 676

∠QPR  = 90°

[By Converse of Pythagoras theorem]

Hence the value of ∠QPR  = 90°.

HOPE THIS WILL HELP YOU....