What is the ratio of a square's area to the area of a square constructed on its diagonal?
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Answer: D. 1:2
Explanation
The original square has an area equal to side length squared using standard geometric principles. Constructing a square on the diagonal creates a new figure with side length multiplied by root two. Squaring the new diagonal side dimension results in twice the original area yielding a one to two ratio. The diagonal of any square divides the interior into two identical right angled triangles. Pythagoras theorem establishes that a square diagonal length equals the side length multiplied by root two. Comparing two geometric areas requires setting up a direct ratio of their numerical square values.
Property developers use diagonal measurements to ensure building foundations maintain perfect square alignment. Computer graphics algorithms scale geometric shapes by applying proportional scaling factors to diagonal bounds. Carpenters check structural squareness by measuring opposing corners to verify equal diagonal distances. Option A proposes a two to five ratio which incorrectly scales the geometric dimensions of the figures. Option B suggests a three to four ratio that lacks any valid geometric derivation from side lengths. Option C offers a three to five proportion which fails to reflect the square root relationship.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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