Two squares have perimeters of 48 cm and 20 cm. Find the perimeter and diagonal of a square whose area equals their combined sum.
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Answer: B. 13√2 cm
Explanation
Combining the areas of the two smaller squares yields a total combined area of one hundred sixty-nine. Extracting the square root of one hundred sixty-nine determines the side length of the new square as thirteen. Multiplying the side length of thirteen by the square root of two yields the exact diagonal measurement. The perimeter of a square equals four times its side length, allowing side determination from perimeter. The area of a square is calculated by squaring the length of any of its equal sides. The diagonal of any square equals its side length multiplied by the square root of two.
Option A suggests fifteen root two which corresponds to an incorrect combined square area calculation. Option C suggests sixteen root two which overestimates the side length derived from the combined areas. Option D suggests seventeen root two which represents an incorrect higher sum of square areas.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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