for the triangles to be similar by the sss similarity theorem, what must be the value of $y$?

18
20
24
26

Question

for the triangles to be similar by the sss similarity theorem, what must be the value of $y$?

18
20
24
26

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" ], "new_concepts": [ "SSS Similarity Theorem" ], "current_concepts": [ "Similar Triangles", "SSS Similarity Theorem" ] } ## Identify corresponding sides of the triangles Using the *Similar Triangles* knowledge point $$ \begin{aligned} &\triangle ABC \sim \triangle PQR\ &\text{Sides of } \triangle ABC: AB = 10, \quad BC = 10, \quad CA = 14\ &\text{Sides of } \triangle PQR: PQ = y, \quad QR = y, \quad RP = 28 \end{aligned} $$ ## Set up the similarity ratio Using the *Similar Triangles* knowledge point $$ \begin{aligned} &\frac{CA}{RP} = \frac{AB}{PQ} = \frac{BC}{QR}\ &\frac{14}{28} = \frac{10}{y} \end{aligned} $$ ## Solve for y Using the *Similar Triangles* knowledge point $$ \begin{aligned} &\frac{1}{2} = \frac{10}{y}\ &y = 20 \end{aligned} $$

(A) 18

(B) 20

(C) 24

(D) 26

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

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QUESTION IMAGE

Question

Explanation:

Identify corresponding sides of the triangles

Set up the similarity ratio

Solve for y

Answer: