A parallelogram has an area of 128 sq m and an altitude twice its corresponding base. Find the base length_________?
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Answer: A. 8 m
Explanation
The geometric area of a parallelogram is calculated by multiplying its base length by its corresponding altitude. Substituting the given condition where the altitude equals twice the base gives two times the base squared equals one hundred twenty-eight. Dividing by two gives a base squared value of sixty-four, which results in a base length of eight meters. A parallelogram is a quadrilateral with opposite sides parallel, and its area formula is base times height. Algebraic substitution allows geometric word problems to be solved by expressing height in terms of the base. Extracting the square root of a positive area product yields the primary linear dimension of the geometric shape.
Option B yields an area of two hundred square meters when applying the altitude twice condition. Option C results in an area of seventy-two square meters, which is well below the required one hundred twenty-eight. Option D produces an area of two hundred eighty-eight square meters, vastly exceeding the given limit.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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