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Problem 138


Problem 138


Special isosceles triangles

Consider the isosceles triangle with base length, b = 16, and legs, L = 17.

By using the Pythagorean theorem it can be seen that the height of the triangle, h = √(172 − 82) = 15, which is one less than the base length.

With b = 272 and L = 305, we get h = 273, which is one more than the base length, and this is the second smallest isosceles triangle with the property that h = b ± 1.

Find ∑ L for the twelve smallest isosceles triangles for which h = b ± 1 and b, L are positive integers.


特殊等腰三角形

考虑底为b = 16,腰为L = 17的等腰三角形。

使用毕达哥拉斯定理,我们可以求出三角形的高是h = √(172 − 82) = 15,恰好比底长小1。

当b = 272而L = 305时,可以算出h = 273,恰好比底长大1,而且这是满足性质h = b ± 1的三角形中第二小的。

对于最小的12个满足h = b ± 1且b,L均为正整数的等腰三角形,求∑ L。