question 15 of 25

in the diagram below, $\delta abc \sim \delta dec$. what is the value of $x$?

a. 22
b. 26
c. 28
d. 24

Question

question 15 of 25

in the diagram below, $\delta abc \sim \delta dec$. what is the value of $x$?

a. 22
b. 26
c. 28
d. 24

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Similar Triangles", "Corresponding Sides Ratio" ], "new_concepts": [], "current_concepts": [ "Similar Triangles", "Corresponding Sides Ratio" ] } ## Identify corresponding sides Using the **Similar Triangles** knowledge point $$ \Delta ABC \sim \Delta DEC \implies \frac{AB}{DE} = \frac{AC}{DC} $$ ## Set up the proportion Using the **Corresponding Sides Ratio** knowledge point $$ \begin{aligned} &AB = 42,\quad DE = 6\ &AC = x,\quad DC = 32 - x\ &\frac{42}{6} = \frac{x}{32 - x} \end{aligned} $$ ## Simplify the ratio Using the **Corresponding Sides Ratio** knowledge point $$ 7 = \frac{x}{32 - x} $$ ## Solve for x Using the **Corresponding Sides Ratio** knowledge point $$ \begin{aligned} &7(32 - x) = x\ &224 - 7x = x\ &224 = 8x\ &x = 28 \end{aligned} $$

A. 22

B. 26

C. 28

D. 24

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Similar Triangles" ] }

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QUESTION IMAGE

Question

Explanation:

Identify corresponding sides

Set up the proportion

Simplify the ratio

Solve for x

Answer: