light oj 1043(数学 + 三角形面积与边之比)

1043 - Triangle Partitioning

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Time Limit: 0.5 second(s)

Memory Limit: 32 MB

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	Output for Sample Input
4 100 100 100 2 10 12 14 1 7 8 9 10 8.134 9.098 7.123 5.10	Case 1: 81.6496580 Case 2: 7.07106781 Case 3: 6.6742381247 Case 4: 7.437454786

 

PROBLEM SETTER: JANE ALAM JAN

简单的数学知识，相似三角形 边长之比等于面积只比的平方。

            AD/AB =  sqrt( S(ADE)/S(ABC));

#include<iostream>
#include<stdio.h>
#include<string.h>
#include<math.h>
#include<algorithm>
#include<queue>
typedef long long ll;
using namespace std;
#define INF 0x3f3f3f3f
typedef long long ll;

int main()
{
int T,cas=1;
double AB,AC,BC,p;
double ans;
scanf("%d",&T);
while(T--)
{
scanf("%lf%lf%lf%lf",&AB,&AC,&BC,&p);
ans=1.0*AB*sqrt(p/(p+1));
printf("Case %d: %.7f\n",cas++,ans);
}
return 0;
}