What is the ratio of a square's area to the area of a square built on its diagonal_________?
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Answer: D. 1:2
Explanation
The area of a standard square with side length x is expressed algebraically as x squared. A square constructed on the diagonal of side length x root two yields an area of two x squared. Forming the ratio of the original area to the diagonal square area gives one x squared to two x squared. The diagonal of a square divides it into two congruent right angled triangles with side ratio one to root two. Squaring the diagonal length of x root two produces two times x squared. Geometric ratios compare dimensional properties by expressing them in simplified fractional terms.
Architects use diagonal square proportions when designing symmetrical floor plans and pavilions. Geometrical proofs often analyze embedded shapes to establish fundamental area scaling ratios. Tile contractors calculate material scaling factors when rotating square tiles along their diagonal axes. Option a suggests an incorrect scaling ratio that contradicts basic Pythagorean theorem geometry. Option b assumes a fractional side ratio not supported by square diagonal properties. Option c represents an arbitrary ratio unrelated to the mathematical properties of square diagonals.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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