annabelle measured her bedroom as $11\text{ ft} \times 13\text{ ft}$, which is $143\text{ square feet}$. she wants to change the units to square inches. which statements should she consider when converting? check all that apply.

there are 12 inches in every foot.
the length and width will change by a factor of $1.2 \times 10^1$.
the length and width will change by a factor of $1.2 \times 10^0$.
the area will change by a factor of $(1.2 \times 10^1)(1.2 \times 10^1) = 1.44 \times 10^2 = 144$, since area is length times width.
the area will change by a factor of $2(1.2 \times 10^1) = (2 \times 10^1)(1.2 \times 10^1) = 2.4 \times 10^2 = 240$, since both the length and width increase by that factor.

Question

annabelle measured her bedroom as $11\text{ ft} \times 13\text{ ft}$, which is $143\text{ square feet}$. she wants to change the units to square inches. which statements should she consider when converting? check all that apply.

there are 12 inches in every foot.
  the length and width will change by a factor of $1.2 \times 10^1$.
  the length and width will change by a factor of $1.2 \times 10^0$.
  the area will change by a factor of $(1.2 \times 10^1)(1.2 \times 10^1) = 1.44 \times 10^2 = 144$, since area is length times width.
  the area will change by a factor of $2(1.2 \times 10^1) = (2 \times 10^1)(1.2 \times 10^1) = 2.4 \times 10^2 = 240$, since both the length and width increase by that factor.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Units of Measurement", "Dimensional Analysis", "Area Unit Conversion", "Scientific Notation" ], "new_concepts": [], "current_concepts": [ "Units of Measurement", "Dimensional Analysis", "Area Unit Conversion", "Scientific Notation" ] } ## Analyze linear conversion factors $$ \begin{aligned} &1\text{ ft} = 12\text{ in} = 1.2 \times 10^1\text{ in} \end{aligned} $$ ## Analyze area conversion factors $$ \begin{aligned} &\text{Area factor} = (1.2 \times 10^1) \times (1.2 \times 10^1) = 1.44 \times 10^2 = 144 \end{aligned} $$ ## Evaluate given statements $$ \begin{aligned} &\text{Statement 1: "There are 12 inches in every foot." } ightarrow \text{True} \ &\text{Statement 2: "The length and width will change by a factor of } 1.2 \times 10^1\text{." } ightarrow \text{True} \ &\text{Statement 3: "The length and width will change by a factor of } 1.2 \times 10^0\text{." } ightarrow \text{False} \ &\text{Statement 4: "The area will change by a factor of } (1.2 \times 10^1)(1.2 \times 10^1) = 1.44 \times 10^2 = 144\text{..." } ightarrow \text{True} \ &\text{Statement 5: "The area will change by a factor of } 2(1.2 \times 10^1)\text{..." } ightarrow \text{False} \end{aligned} $$

There are 12 inches in every foot.

The length and width will change by a factor of $1.2 \times 10^1$.

The length and width will change by a factor of $1.2 \times 10^0$.

The area will change by a factor of $(1.2 \times 10^1)(1.2 \times 10^1) = 1.44 \times 10^2 = 144$, since area is length times width.

The area will change by a factor of $2(1.2 \times 10^1) = (2 \times 10^1)(1.2 \times 10^1) = 2.4 \times 10^2 = 240$, since both the length and width increase by that factor.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Area Unit Conversion" ] }

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Explanation:

Analyze linear conversion factors

Analyze area conversion factors

Evaluate given statements

Answer: