if triangles $def$ and $npq$ are similar, what is the length of side $q$?

* enter the answer as a fraction.

provide your answer below:

$q = $

Question

if triangles $def$ and $npq$ are similar, what is the length of side $q$?

* enter the answer as a fraction.

provide your answer below:

$q = $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Proportional Reasoning" ], "new_concepts": [ "Similar Triangles" ], "current_concepts": [ "Proportional Reasoning", "Similar Triangles" ] } ## Set up the similarity ratio $$ \triangle DEF \sim \triangle NPQ \implies \frac{DE}{NP} = \frac{EF}{PQ} = \frac{DF}{NQ} $$ ## Identify corresponding sides and values $$ \begin{aligned} &DE = \frac{5}{2},\quad DF = 7,\quad EF = d\ &NP = q,\quad NQ = 9,\quad PQ = \frac{11}{2}\ &\frac{DE}{NP} = \frac{DF}{NQ} \implies \frac{\frac{5}{2}}{q} = \frac{7}{9} \end{aligned} $$ ## Solve for q $$ \begin{aligned} &7q = 9 \cdot \frac{5}{2}\ &7q = \frac{45}{2}\ &q = \frac{45}{14} \end{aligned} $$ If triangles $DEF$ and $NPQ$ are similar, what is the length of side $q$? $q =$ $\frac{45}{14}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Similar Triangles" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the similarity ratio

Identify corresponding sides and values

Solve for q

Answer: