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Question

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

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Solution

We are given two triangles ΔABC and ΔPQR such that ΔABCΔPQR.
Corresponding sides will be proportional.
ABPQ=BCQR=ACPR
Here, 12×BC12×QR=BMQN
ABPQ=BMQN
Since both the triangles ΔABC and ΔPQR are similar, there angles will be equal
A = P, B = Q and C = R
In ΔABM and ΔPQN,
ABPQ=BMQN (Proved above)
B = Q
ΔABMΔPQN [By SAS similarity]
Given: AM = PO = 5 cm
Area of ΔABCArea of ΔPQR=AB2PQ2=925
ABPQ=35
ABPQ=AMPN=35
55+ON=35
25=15+3(ON)
ON=103
3(ON)=10cm
Hence the length of 3(ON) is 10 cm.

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