Question

The areas of two similar triangles are 81cm & 49cm respectively. Find the ratio of the corresponding medians.

Answer 1

Answer:

Given : ΔABC ~ ΔPQR

Area (ΔABC) = 81 cm2

Area (ΔPQR) = 49 cm2

Figure:

And AD and PS are the altitudes

By area of similar triangle theorem: The ratio of the areas of two similar triangles equal to the ratio of squares of the corresponding sides of triangles.

We also know that:

So, Ratio of altitudes = 9/7

Hence, ratio of altitudes = Ratio of medians = 9:7