A square has a 4√2 cm diagonal. What is the diagonal of another square whose area is double the first__________?
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Answer: A. 8cm
Explanation
The side length of the original square is derived from its given diagonal measurement. Doubling the area of the first square gives a new area value of thirty two square units. Calculating the diagonal of the new square yields an exact length of eight centimeters. The diagonal of a square equals its side length multiplied by the square root of two. The area of a square is calculated by squaring its side length or squaring its diagonal and halving. Geometric scaling principles show that doubling an area multiplies linear dimensions by root two.
Square measurements are fundamental in tiling, construction, and land partitioning projects. Architects use diagonal calculations to ensure structural squareness and precise room layouts. Geometric proportions help scale drawings and blueprints accurately up or down in size. Option b introduces an unnecessary radical that overestimates the correct diagonal length. Option c suggests sixteen centimeters which represents an incorrect area scaling calculation. Option d matches the original square diagonal instead of the newly scaled square.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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