Diffcult Maths Question !!!
2009-03-08 9:17 pm
Cynthia wants to design a rectangular playground of 616 square metres and she also wants to have a fence built around it. However, she only has enough fence materials for a playground of 100 metres in perimetre. What should be the dimensions of the playground? (Problems similar to this question were studied and solved by the Babylonians more than four thousand years ago)
回答 (1)
2009-03-08 9:42 pm
✔ 最佳答案
Let the dimensions of the playground be a * b, let a>=b ,thenab = 616
(a+b) * 2 = 100,
a + b = 50 ...(1)
(a - b)^2 = (a+b)^2 - 4ab = 50^2 - 4 * 616 = 36
a - b = 6 ...(2)
(1)+(2) :
2a = 56 , a = 28
b = 50-28 = 22
so the dimensions of the playground is 28 metres * 22 metres .
It should be the method of Babylonians .
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