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A flowerbed of uniform width is developed around a rectangular patch of grass such that the outer length of the flowerbed is two-thirds more than the length of the rectangular patch and the outer breadth of the flowerbed is 100 percent greater than the breadth of the rectangular patch. If the area of the flowerbed is 8 square units more than twice the area of the rectangular patch, what is the area of the rectangular patch of grass?
  • a)
    6 square units
  • b)
    20 square units
  • c)
    24 square units
  • d)
    80 square units
  • e)
    Cannot be determined
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A flowerbed of uniform width is developed around a rectangular patch o...
Given:
Representing the given scenario visually.
  • Let the length of the rectangular patch of grass be Lp and the breadth be Bp
  • Let the uniform width of the flowerbed be w
  • And let the outer length of the flowerbed be LF and the breadth be BF
  • (Area of flower bed) = 2(Area of patch) + 8
    • That is, (Area of outer rectangle – Area of patch) = 2(Area of patch) +8
To find : Area of the patch
Approach:
  1.  Area of the patch = Lp *Bp
    1. So, we need to find the value of L and B or at least of their product to be able to do this​
  2. By using Equations (1), (2) and (3) together, we’ll be able to find the value of product Lp *Bp
Looking at the answer choices, we see that the correct answer is Option C
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A flowerbed of uniform width is developed around a rectangular patch of grass such that the outer length of the flowerbed is two-thirds more than the length of the rectangular patch and the outer breadth of the flowerbed is 100 percent greater than the breadth of the rectangular patch. If the area of the flowerbed is 8 square units more than twice the area of the rectangular patch, what is the area of the rectangular patch of grass?a)6 square unitsb)20 square unitsc)24 square unitsd)80 square unitse)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer?
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