the area of a triangle is 1,440 \text{ cm}^2. the base of the triangle is 5 times the height. what is the height of the triangle?

$12 \text{ cm}$
$24 \text{ cm}$
$46 \text{ cm}$
$60 \text{ cm}$

Question

the area of a triangle is 1,440 \text{ cm}^2. the base of the triangle is 5 times the height. what is the height of the triangle?

$12 \text{ cm}$
$24 \text{ cm}$
$46 \text{ cm}$
$60 \text{ cm}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Modeling Interpretation", "Quadratic Equation Formulation" ], "new_concepts": [ "Triangle Area Formula" ], "current_concepts": [ "Quadratic Modeling Interpretation", "Quadratic Equation Formulation", "Triangle Area Formula" ] } ## Formulate the quadratic equation $$ \begin{aligned} A &= \frac{1}{2} \cdot b \cdot h \ A &= 1440 \ b &= 5h \ 1440 &= \frac{1}{2} \cdot (5h) \cdot h \ 1440 &= 2.5h^2 \end{aligned} $$ ## Solve for the height $$ \begin{aligned} h^2 &= \frac{1440}{2.5} \ h^2 &= 576 \ h &= \sqrt{576} \ h &= 24 \end{aligned} $$

12 cm

24 cm

46 cm

60 cm

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Equation Formulation" ] }

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QUESTION IMAGE

Question

Explanation:

Formulate the quadratic equation

Solve for the height

Answer: