9. the lengths of corresponding sides of 2 similar right triangles are in the ratio 4:5. the hypotenuse of the smaller triangle is 24 inches long. how many inches long is the hypotenuse of the larger triangle?
a. 1.25
b. 20
c. 25
d. 30

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Ratio and Proportion", "Similar Triangles" ], "new_concepts": [], "current_concepts": [ "Ratio and Proportion", "Similar Triangles" ] } ## Set up the proportion for corresponding sides $$ \frac{\text{Side of smaller triangle}}{\text{Side of larger triangle}} = \frac{4}{5} $$ ## Substitute the given hypotenuse and solve $$ \begin{aligned} \frac{24}{x} &= \frac{4}{5} \ 4x &= 120 \ x &= 30 \end{aligned} $$

A. 1.25

B. 20

C. 25

D. 30

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

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Question

Explanation:

Set up the proportion for corresponding sides

Substitute the given hypotenuse and solve

Answer: