LightOJ 1043 - Triangle Partitioning【数学】

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本文详细介绍了如何解决LightOJ1043-TrianglePartitioning问题，通过给定的三角形边长和面积比例，计算得到AD的长度。该题目的解法涉及几何和数学原理，旨在提高读者在处理此类问题时的算法思维能力。

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LightOJ 1043 - Triangle Partitioning

Time Limit:500MS Memory Limit:32768KB 64bit IO Format:%lld & %llu

Submit Status Practice LightOJ 1043

Description

See the picture below.

You are given AB, AC and BC. DE is parallel to BC. You are also given the area ratio between ADE and BDEC. You have to find the value of AD.

Input

Input starts with an integer T (≤ 25), denoting the number of test cases.

Each case begins with four real numbers denoting AB, AC, BC and the ratio of ADE and BDEC(ADE / BDEC). You can safely assume that the given triangle is a valid triangle with positive area.

Output

For each case of input you have to print the case number and AD. Errors less than 10^-6 will be ignored.

Sample Input

100 100 100 2

10 12 14 1

7 8 9 10

8.134 9.098 7.123 5.10

Sample Output

Case 1: 81.6496580

Case 2: 7.07106781

Case 3: 6.6742381247

Case 4: 7.437454786

AC-code：

#include<cstdio>
#include<cmath>
int main()
{
	int T,i;
	double ans,a,b,c,d;
	scanf("%d",&T);
	for(i=1;i<=T;i++)
	{
		scanf("%lf%lf%lf%lf",&a,&b,&c,&d);
		ans=a/sqrt((d+1)/d);
		printf("Case %d: %.7lf\n",i,ans);
	}
	return 0;
}