A square built on a rectangle's diagonal has an area 108 1/3% greater than the rectangle. Given a 28-unit rectangle perimeter, find the difference between its sides.
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Answer: D. 2
Explanation
Relating the area of a square built on a rectangle diagonal to the rectangle dimensions forms a system of equations. Using the given rectangle perimeter of twenty-eight units establishes the sum of length and breadth as fourteen. Solving the simultaneous equations yields rectangle sides whose absolute difference evaluates to exactly two units. Pythagoras theorem links the diagonal of a rectangle directly to the sum of the squares of its sides. Rectangle perimeter equals twice the sum of its length and breadth dimensions. Simultaneous algebraic equations allow solvers to find individual side lengths from perimeter and area conditions.
Structural engineers use diagonal calculations to ensure rectangular building frames maintain rigid right angles. Carpenters check diagonal measurements to verify that constructed wooden frames are perfectly square. Advanced geometric word problems strengthen algebraic problem-solving and spatial visualization skills. Option A overestimates the side difference by using incorrect perimeter proportion assumptions. Option B suggests a large side difference that contradicts the perimeter sum of fourteen units. Option C proposes an alternate difference value that fails to satisfy the diagonal area relationship.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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