Relation between Area and Sides of Similar Triangles
If ABC and Δ ...
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 ___
Open in App
Solution
We are given two triangles i.e. ΔABC and ΔPQR such that ΔABC∼ΔPQR 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 ΔABM∼ΔPQN [ SAS similarity] Given AM = PO = 5 cm ⇒AreaofΔABCAreaofΔPQR=AB2PQ2=925⇒ABPQ=35 ⇒ABPQ=AMPN=35⇒55+ON=35 Then 25=15+3(ON)ON=1033(ON)=10cm Hence the length of 3(ON) is 10 cm.