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6. In the figure, PQR is a triangle right angled atPX : XQ = 1 : 2, Calculate the lengths of PR and QR.Q and Y 11 OR If PQ = 6 cm, PY= 4 cm, and

Answer»

BASIC PROPORTIONALITY THEOREM (BPT) : If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points then the other two sides are divided in the same ratio. This is also known as Thales theorem.

GIVEN:∠Q= 90° , XY || QR, PQ = 6cm, PY = 4cm & PX : XQ = 1 : 2

Since, XY || QR,PX/XQ = PY/YR

[ By Thales theorem (BPT)]½ = PY/YR [PX : XQ = 1 : 2]½ = 4 /(PR - PY)

[YR= PR - PY]

½ = 4 /(PR - 4)PR - 4 = 2 × 4PR - 4 = 8PR = 8 +4

PR = 12cm

In right ∆PQR,PR² = PQ² + QR²

[ By Pythagoras theorem]12² = 6² + QR² [Given : PQ= 6cm]144 = 36 + QR²144 - 36 + QR²108 = QR²

QR =√108 =√ 3×36 = 6√3 cm

Hence, the lengths of PR and QR is 12 cm.& 6√3 cm.


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