### Special isosceles triangles题号：138 难度： 45 中英对照

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.

### Code

public final class p138 {
public static void main(String[] args) {
long start=System.nanoTime();
String result = run();
long end=System.nanoTime();
System.out.println(result);
System.out.println( (end-start)/1000000 + "ms" );
}

static public String run(){
long res=0;
long x=0;
long y=1;
for(int i=0;i<12;i++){
long xnew=-9*x-4*y-4;
long ynew=-20*x-9*y-8;
x=xnew;
y=ynew;
res+=Math.abs(y);
}
return ""+res;
}

}
1118049290473932
0ms