A rectangular field's length is twice its width and contains an 8m square pond. If the pond's area is 1/8th of the field, what is the field's length?
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Answer: B. 32 m
Explanation
An eight meter square pond has an area equal to sixty four square meters. Multiplying sixty four square meters by eight gives the total field area of five hundred twelve. Solving the equation where length equals twice the width reveals a length of thirty two meters. The area of any square is found by squaring the length of its side. Geometric proportions allow scaling smaller embedded shapes to find total enclosing region dimensions. A rectangle with length twice its width satisfies the algebraic expression two w squared.
Landscape architects use area ratios when planning water features inside public parks and gardens. Real estate developers calculate property boundaries relative to internal structural features like swimming pools. Agricultural zoning often requires proportional divisions of land for irrigation and cultivation purposes. Option a produces an incorrect area because thirty one does not yield a clean square root. Option c results in a field area that is too small for the pond proportions. Option d implies a different length to width ratio than specified in the problem statement.
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- Mathematics
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- Mathematics
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- medium
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