Question

sides of two similar triangle are in the ratio of 4:9 corresponding median of these triangle are in the ratio​

Answer 1

Answer:

4:9

two triangles ABC and PQR

draw BD (median ) in triangle ABC

we can prove that ABE is similar to ace

similarly in PQR ( i.e PQS similar to PRS)

equating both we get ABE similar to PQS

AB/PQ = BE/QS

4/9 = BE/QS

BE and QS are medians

ratio of medians is 4:9

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Answer 2

Step-by-step explanation:

Given: Sides of two similar triangle are in the ratio of 4:9.

To find:The ratio of corresponding median of these triangle are ?

Solution:

Tip: If two triangles are similar than ratio of their corresponding sides are equal and equal to ratio of their corresponding medians.

Let ∆ABC and ∆PQR are similar and AM and PS are one median of respectively.

$\frac{AB}{PQ} =\frac{CB}{QR} =\frac{AC}{PR} =\frac{4}{9}$

According to theorem discussed in 'Tip';

$\frac{AB}{PQ} =\frac{CB}{QR} =\frac{AC}{PR}=\frac{AM}{PS} =\frac{4}{9}$

Final answer:

Ratio of their corresponding median are 4:9.

Hope it helps you.

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