MATH!! (S1-3)

2012-04-05 5:05 am
How many different isosceles triangles are possible if the perimeter is 120 and all side lengths are integers?????Given that X/2 = Y/3 = Z/11 = 3X - Y + 4Z / T Find T

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回答 (1)

2012-04-05 6:08 am
✔ 最佳答案
1)Let L , L , B be 3 sides of the isosceles triangle , then2L + B = 120 ......(1)
{
2L > B ......(2)
(1) + (2) :4L + B > 120 + B
4L > 120
L > 30So L = 31 , 32 , 33 , ... , 58 , 59Total 59 - 31 + 1 = 29 different isosceles triangles.
2)X/2 = Y/3 = Z/11 = 3X - Y + 4Z / T
So X : Y : Z = 2 : 3 : 11
Let X = 2k , Y = 3k , Z = 11k , then(X/2 = Y/3 = Z/11) = 3X - Y + 4Z / T
(2k/2 = 3k/3 = 11k/11) = 3X - Y + 4Z / Tk = 3(2k) - 3k + 4(11k) / T1 = 6 - 3 + 44/T- 2 = 44/TT = - 22


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