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# The areas of two similar triangles are 100 cm2 and 64cm2 respectively. If a median of the smaller triangle is 5.6 cm, find the corresponding median of the other.

Let ABC and DEF are two similar triangles such that ar (ABC) =100cm2 and ar (DEF) = 64cm2

Also, let AM and DN are medians of ABC and DEF respectively.

Now in ABC and DEF

B = E [ABC ~ DEF]

and

ABC ~ DEF [by SAS similarity]

…(i)

Now, as ABC ~ DEF

We know that, the ratio of two similar triangles is equal to the square of the ratio of their corresponding sides.

[from (i)]

AM = 7cm

Hence, the length of the other median is 7cm.

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