triangle abc is congruent to triangle xyz. in $\delta abc$, $ab = 12\text{ cm}$ and $ac = 14\text{ cm}$. in $\delta xyz$, $yz = 10\text{ cm}$ and $xz = 14\text{ cm}$.

what is the perimeter of $\delta abc$?

36 cm
38 cm
40 cm
50 cm

Question

triangle abc is congruent to triangle xyz. in $\delta abc$, $ab = 12\text{ cm}$ and $ac = 14\text{ cm}$. in $\delta xyz$, $yz = 10\text{ cm}$ and $xz = 14\text{ cm}$.

what is the perimeter of $\delta abc$?

36 cm
38 cm
40 cm
50 cm

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Triangle Congruence", "Corresponding Parts" ], "new_concepts": [ "Perimeter of Congruent Triangles" ], "current_concepts": [ "Triangle Congruence", "Corresponding Parts", "Perimeter of Triangles" ] } ## Identify corresponding sides of congruent triangles $$ \begin{aligned} &\triangle ABC \cong \triangle XYZ \ &AB = XY = 12\text{ cm} \ &AC = XZ = 14\text{ cm} \ &BC = YZ = 10\text{ cm} \end{aligned} $$ ## Calculate the perimeter of triangle ABC $$ \begin{aligned} P_{\triangle ABC} &= AB + BC + AC \ P_{\triangle ABC} &= 12 + 10 + 14 \ P_{\triangle ABC} &= 36\text{ cm} \end{aligned} $$

(A) 36 cm

(B) 38 cm

(C) 40 cm

(D) 50 cm

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Congruence" ] }

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Question

Explanation:

Identify corresponding sides of congruent triangles

Calculate the perimeter of triangle ABC

Answer: