If the diagonal of a square is decreased by 15%, then by what percent does the area of the square decrease?


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Answer:

27.75%

Step by Step Explanation:
  1. Let the length of the diagonal of the square be d. Length of the side of the square will then be ÷ d / √2, and the area of the square will be (d / √2) × (d / √2) = 0.5d2
  2. After reducing the length of the diagonal by 15%, the new length of the diagonal will be:
    = d -  
    15
    100
     d
    = 0.85d
  3. Hence, the new area will be 0.5(0.85d)2 = 0.5 × 0.7225d2.
  4. Decrease in the area = Old area - New area
    = 0.5 d2 - 0.5 × 0.7225d2
    = 0.5 × (1 - 0.7225) d2
    = 0.5 × 0.2775 d2
  5. Percentage decrease in the area =  
    Decrease in the area
    Old area
      × 100 %
    =  
    0.5 × 0.2775 d2
    0.5 d2
      × 100 %
    = 0.2775 × 100 %
    = 27.75%
  6. Hence, when the diagonal of the square is decreased by 15%, then the area of the square decreases by 27.75%.

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