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Question
In the figure, given below, PQR is a right-angle triangle right angled at Q. XY is parallel to QR, PQ = 6 cm, PY = 4 cm and PX : XQ = 1 : 2. Calculate the lengths of PR and QR.
Solution
Given that `(PX)/(XQ) = 1/2` and XY || QR
So, `(PX)/(XQ) = (PY)/(YR) = 1/2`
Since PY = 4 cm, YR = 8 cm.
Hence, PR = 12 cm
Since ΔPQR is a right-angled triangle
By Pythagoras theorem,
QR2 = PR2 – PQ2
`=>` QR2 = 122 – 62
`=>` QR2 = 144 – 36
`=>` QR2 = 108
`=>` QR = 10.39 cm
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