A square's perimeter is twice a rectangle's perimeter. The rectangle's area is 480 sq cm. Find the square's area.
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Answer: D. Cannot be determined
Explanation
Calculating a square's area from a rectangle's perimeter requires knowing specific linear dimensions of both shapes. A constant ratio between perimeters does not provide enough distinct equations to isolate length and breadth separately. Without knowing either individual dimension or the exact perimeter value, the square's area remains entirely undetermined. System of equations require an equal number of independent conditions to solve for multiple unknown variables. Area and perimeter formulas for rectangles involve two independent variables representing length and breadth dimensions. Geometric problems lacking sufficient numerical constraints often yield multiple valid solutions or remain indeterminate.
Architects cannot finalize material cost estimates for building footprints when blueprints lack complete dimensional specifications. Surveyors cannot compute total property acreage when legal boundary descriptions omit essential linear distance measurements. Engineers cannot determine structural stress distributions without complete geometric profiles of load-bearing members. Option A suggests two hundred square centimeters which assumes arbitrary unproven dimensions for the rectangle. Option B suggests seventy-two square centimeters which relies on unverified assumptions about perimeter ratios. Option C suggests one hundred sixty-two square centimeters which lacks mathematical justification from given data.
- Subject
- Mathematics
- Category
- Mathematics
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- Difficulty
- medium
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