Question

Sides of two similar triangles are in the ratio 4:9. Corresponding medians of these triangles

are in the ratio:

a. 2:3 

b. 4:9 

c. 81:16 

d. 16:81​

Answer 1

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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