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。