If DB= 9 and DC= 4, find the length of segment DA

This question is based on line segment. Therefore, the value of DA  is 6.

Given:

DB= 9 and DC= 4

We need to determined the length of DA.

According to question,

In given figure, we observe that  both the triangles are similar.Therefore we make proportion as below,

Substitute the given value in above proportion.We get,

Now, solve it further,

Thus, the value of DA is  6.

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 DA = 6

Explanation:

The triangles are similar, allowing us to make the proportion below

DB/DA = DA/DC

Plug in the given values. Cross multiply and solve for x

DB/DA = DA/DC

9/DA = DA/4

9*4 = (DA)*(DA)

36 = (DA)^2

(DA)^2 = 36

DA = sqrt(36)

DA = 6

The length of DA is exactly the geometric mean of the lengths BD and DC

geometric mean of x and y = sqrt(x*y)

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