A rectangle's length is two-fifths of a circle's radius. The circle's radius matches the side of a square with a 1225 sq unit area. What is the rectangle's area given a 10-unit breadth?
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Answer: A. 140
Explanation
The square root of twelve hundred twenty five establishes the circle radius as thirty five. Taking two fifths of thirty five gives the exact length of the target rectangle. Multiplying the calculated length of fourteen by the breadth of ten yields one hundred forty. The area of a square equals the square of its side length measurement. A circle radius serves as a dimensional bridge linking geometric shapes together. Rectangle area is calculated by multiplying its length measurement by its breadth measurement.
Urban planners frequently convert proportional measurements when scaling architectural blueprints into physical structures. Engineering designs often require linking circular components with rectangular support frameworks efficiently. Manufacturing processes rely on accurate dimensional conversions to cut raw materials without waste. Option b results from an arithmetic error during the fractional multiplication of the radius. Option c emerges if the breadth is incorrectly applied as a different multiplier value. Option d occurs when failing to simplify the fraction properly during length calculation steps.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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