question 36 of 40

if $\triangle abc \sim \triangle def$ and the scale factor from $\triangle abc$ to $\triangle def$ is $\frac{1}{7}$, what are the lengths of $\overline{de}$, $\overline{ef}$, and $\overline{df}$, respectively?

a. 4, 5, 2
b. 35, 21, 42
c. 21, 7, 28
d. 196, 98, 245

Question

question 36 of 40

if $\triangle abc \sim \triangle def$ and the scale factor from $\triangle abc$ to $\triangle def$ is $\frac{1}{7}$, what are the lengths of $\overline{de}$, $\overline{ef}$, and $\overline{df}$, respectively?

a. 4, 5, 2
b. 35, 21, 42
c. 21, 7, 28
d. 196, 98, 245

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Scale Factor", "Similar Triangles" ], "new_concepts": [], "current_concepts": [ "Scale Factor", "Similar Triangles" ] } ## Identify corresponding sides of similar triangles $$ \begin{aligned} &\triangle ABC \sim \triangle DEF \ &AB \text{ corresponds to } DE \ &BC \text{ corresponds to } EF \ &AC \text{ corresponds to } DF \end{aligned} $$ ## Apply the scale factor to find the lengths $$ \begin{aligned} &k = \frac{1}{7} \ &DE = k \cdot AB = \frac{1}{7} \cdot 28 = 4 \ &EF = k \cdot BC = \frac{1}{7} \cdot 35 = 5 \ &DF = k \cdot AC = \frac{1}{7} \cdot 14 = 2 \end{aligned} $$ ## Match with the given options $$ (DE, EF, DF) = (4, 5, 2) $$

A. 4, 5, 2

B. 35, 21, 42

C. 21, 7, 28

D. 196, 98, 245

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify corresponding sides of similar triangles

Apply the scale factor to find the lengths

Match with the given options

Answer: