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Question

If ABC and PQR are two similar triangles shown in the figure. AM and AN are the medians on ABC and PQR respectively. The ratio of areas of ABC and PQR is 9:25. If AM = PO = 5 cm. Find the value of 3ON.

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Solution

We are given two triangles ABC and PQR such that ABC ~ PQR

Given AM = PO = 5 cm

So, areaofABCareaofPQR = AM2PN2 = 52(5+ON)2 = 925

Take the square root on both sides

Then 55+ON = 35

25 = 15 + 3ON

ON = 103

3ON = 10 cm


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