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The figure shows a rectangle divided into 9 squares. The squares have integral sides and adjacent sides of the rectangle are co-prime. Find the perimeter of the rectangle?
  • a)
    260 unit
  • b)
    178 unit
  • c)
    234 unit
  • d)
    Indeterminable
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The figure shows a rectangle divided into 9 squares. The squares have...
Let the sides of the squares be a, b, ..., i (in ascending order of size - 'a' is not marked in the diagram). We have a + b = c (1), a + c = d (2), c + d = e(3), d + e = f(4), b + c + e = g(5),
b + g = h(6), a + d + f i(7), f+ i = g + h (8). Using (1) - (7) we can solve in terms of a, h, then (8) gives 5a = 2b, so a = 2, b = 5 (must have no common factor). Hence f = 25, h 33, i = 36, sides are 61, 69. So the perimeter will be 2 (61 + 69) = 260 unit.
Hence the correct option is (a)
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The figure shows a rectangle divided into 9 squares. The squares have integral sides and adjacent sides of the rectangle are co-prime. Find the perimeter of the rectangle?a)260 unitb)178 unitc)234 unitd)IndeterminableCorrect answer is option 'A'. Can you explain this answer?
Question Description
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