Question

Sides of two similar triangles are in the ratio4:9.Corresponding medians of these triangles are in the ratio, a) 2:3 b) 4:9 c) 81:16 d) 16:81

Answer 1

Answer:

If two triangles are similar to each other, then the ratio of the areas of these triangles will be equal to the square of the ratio of the corresponding sides of these triangles. It is given that the sides are in the ratio 4:9. Hence, the correct answer is 16 : 81.

Step-by-step explanation:

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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 ?

a) 2:3

b) 4:9

c) 81:16

d) 16:81

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';

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

Option B is correct.

Final answer:

Ratio of their corresponding median are 4:9.

Option B is correct.

Hope it helps you.

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