Q. 95.0( 1 Vote )

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.

Answer :


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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