a teacher asks her students to design a game board for a class project. the dimensions of the boards created by four students are shown below.

angela
length: 20 cm
width: 21 cm
diagonal: 29 cm

bradley
length: 9 in.
width: 9 in.
diagonal: 9 in.

carlton
length: 25 cm
width: 30 cm
diagonal: 35 cm

della
length: 10 in.
width: 12 in.
diagonal: 15 in.

whose game board could be a rectangle?

angela
bradley
carlton
della

Question

a teacher asks her students to design a game board for a class project. the dimensions of the boards created by four students are shown below.

angela
length: 20 cm
width: 21 cm
diagonal: 29 cm

bradley
length: 9 in.
width: 9 in.
diagonal: 9 in.

carlton
length: 25 cm
width: 30 cm
diagonal: 35 cm

della
length: 10 in.
width: 12 in.
diagonal: 15 in.

whose game board could be a rectangle?

angela
bradley
carlton
della

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Pythagorean Theorem", "Pythagorean Triples" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem", "Pythagorean Triples", "Properties of Rectangles" ] } ## Apply the Pythagorean theorem to each student's dimensions $$ \begin{aligned} &\text{Angela: } 20^2 + 21^2 = 400 + 441 = 841 = 29^2 \ &\text{Bradley: } 9^2 + 9^2 = 81 + 81 = 162 eq 9^2 \ &\text{Carlton: } 25^2 + 30^2 = 625 + 900 = 1525 eq 35^2 \quad (1225) \ &\text{Della: } 10^2 + 12^2 = 100 + 144 = 244 eq 15^2 \quad (225) \end{aligned} $$ ## Identify the valid rectangular board $$ \text{Angela's board satisfies } a^2 + b^2 = c^2 $$

Angela

Bradley

Carlton

Della

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Pythagorean Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Apply the Pythagorean theorem to each student's dimensions

Identify the valid rectangular board

Answer: