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a + b = 58

a - b = 16

Thus:

2a = 74

a = 37

b = 21

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a + b = 58

a - b = 16

Thus:

2a = 74

a = 37

b = 21

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The grade is C1

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Suppose the length is L and the breadth is B.

Then since perimeter = 58,

2*(L+B) = 58 so that L+B = 29 that is L = 29-B

Now Area = L*B = 204

That is (29-B)*B = 204

Or B2 - 29B + 204 = 0

which is equivalent to (B-12)*(B-17) = 0

So, using L+B = 29, L and B are 12 and 17.

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There are infinitely many pairs of numbers that can be multiplied to get 58.

Pick and number, A, between -7.616 and 7.616.

Let B = 58/A. Then the definition of A will guarantee that B is not in the range (-7.616, 7.616).


Now A*B = A*58/A = 58 and since

  • the choice of A was arbitrary and
  • the ranges of A and B are distinct so that there is no possibility that a pair (A1, B1) = (B2, A2), each choice of A gives a new pair.

Therefore, there are infinitely many pairs.




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58

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