Question

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

Answer 1

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]

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

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