what is the value of $x$ in the figure below? in this diagram, $\delta abd \sim \delta cad$.

a. $\sqrt{70}$
b. $\sqrt{126}$
c. $\sqrt{45}$
d. 14
e. 45
f. $\frac{9}{14}$

Question

what is the value of $x$ in the figure below? in this diagram, $\delta abd \sim \delta cad$.

a. $\sqrt{70}$
b. $\sqrt{126}$
c. $\sqrt{45}$
d. 14
e. 45
f. $\frac{9}{14}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Similar Right Triangles", "Geometric Mean Theorems" ], "new_concepts": [], "current_concepts": [ "Similar Right Triangles", "Geometric Mean Theorems" ] } ## Identify the given information Using the **Similar Right Triangles** and **Geometric Mean Theorems** knowledge points $$ \begin{aligned} &\Delta ABD \sim \Delta CAD\ &BD = 5\ &CD = 9\ &AD = x \end{aligned} $$ ## Set up the proportion Using the **Similar Right Triangles** and **Geometric Mean Theorems** knowledge points $$ \begin{aligned} &\frac{BD}{AD} = \frac{AD}{CD}\ &\frac{5}{x} = \frac{x}{9} \end{aligned} $$ ## Solve for x Using the **Similar Right Triangles** and **Geometric Mean Theorems** knowledge points $$ \begin{aligned} &x^2 = 5 \cdot 9\ &x^2 = 45\ &x = \sqrt{45} \end{aligned} $$

A. $\sqrt{70}$

B. $\sqrt{126}$

C. $\sqrt{45}$

D. 14

E. 45

F. $\frac{9}{14}$

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QUESTION IMAGE

Question

Explanation:

Identify the given information

Set up the proportion

Solve for x

Answer: