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Question

If ΔABC and ΔPQR are two similar triangles shown in the figure. AM and PN are the medians on ΔABC and ΔPQRrespectively. The ratio of areas of ΔABC and ΔPQR is 9:25. If AM = PO = 5 cm. Find the value of 3(ON) in cm ___

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Solution

We are given two triangles i.e. ΔABC and ΔPQR such that ΔABCΔPQR so, the corresponding ratio of sides and corresponding angles should be equal.
ABPQ=BCQR=ACPR
Also, 12×BC12×QR=BMQN
Since both the triangles i.e. ΔABC and ΔPQR are similar, there angles will be equal i.e. A = P, B = Q and C = R.
In ΔABM and ΔPQN,
ABPQ=BMQN
B = Q
Therefore ΔABMΔPQN [ SAS similarity]
Given AM = PO = 5 cm
Area of ΔABCArea of ΔPQR=AB2PQ2=925ABPQ=35
ABPQ=AMPN=3555+ON=35
Then
25=15+3(ON)ON=1033(ON)=10cm
Hence the length of 3(ON) is 10 cm.

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