Question

In the adjoining figure, PQR, is a right triangle, right angled at Q. X and Y are the points on PQ and QR such that PX : XQ = 1:2 and QY:YQ = 2:1. Prove that 9 (PY^2 + XR^2) =13 PR^2

Please answer fast for 30 points.

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Answer 1

In triangle XRQ
XQ²+QR²=XR²
(2/3PQ)²+QR²=XR²
4/9PQ²+QR²=XR² (1)BY Pythagoras THEOREM
IN TRIANGLE PYR
PQ²+QY²=PY²
PQ²+(2/3QR)²= PY² (2)BY PYTHAGORAS
PQ²+4/9QR²=PY²
IN TRIANGLE PQR
PQ²+QR²=PR² (3)PYTHAGORAS THEOREM
Adding 1 and 2
4/9QR²+QR²+4/9PQ²+PQ²=XR²+PY²
13/9 QR²+ 13/9 PQ ²= XR²+PY²
1/9(13QR²+13PQ²) = XR²+PY²
13(QR²+PQ²) =9(XR²+PY²)
FROM 3 WE GET
13PR²=9(XR²+PY²)

Answer 2

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