Respuesta :

Answer:

D

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{AD}{CD}[/tex] = [tex]\frac{BD}{AD}[/tex] , substitute values

[tex]\frac{x}{13}[/tex] = [tex]\frac{3}{x}[/tex] ( cross- multiply )

x² = 39 ( take the square root of both sides )

x = [tex]\sqrt{39}[/tex] → D

The value of x in the figure showing triangles ABD & triangle CAD is;

x = √39

  • From the given figure showing the triangles, we can say that there are 2 congruent triangles. This is because we are told that ΔABD ≅ ΔCAD and the symbol ≅ means congruent.

Now, corresponding sides of 2 congruent triangles usually have same ratio.

  • Using this concept of congruent triangles, to write the ratio of corresponding sides, we have;

BD/AD = AD/DC

Thus; 3/x = x/13

cross multiply to get;

x² = 13 × 3

x² = 39

take square roots of both sides to get;

x = √39

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