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Let,

ratio of length and width = a:b

Length, L=ax=AB=CD

width, W=bx=AC=BD

where x is the common factor of the ratio.

Now,

here, θ must be in radian.

We know,

arc= angle made by the arc(in radian) * radius

=> AGC=θ*r

=>S=θ*kx

according to question,

2S + 2l = 400

=>2θ.kx + 2ax = 400

=> x=400/(2θk+2a)

Now L=ax & W=bx

#include<stdio.h> 
#include<math.h> 
#include<ctype.h> 
#include<string.h> 
#include<stdlib.h>

  int main() {

    double a, b, k, theta, l, w, common;

    int i, len, m, test;

    char str[1000], first[500], second[500];

    test = 1;

    while (gets(str)) {

      for (i = 0; str[i] != ':'; i++) {

        first[i] = str[i];
      }
      first[i] = '\0';

      for (m = 0; m < strlen(str) - i; m++) {
        second[m] = str[m + i + 1];
      }
      second[m] = '\0';
      a = atoi(first);
      b = atoi(second);
      k = (sqrt(pow(a, 2) + pow(b, 2)) / 2);
      theta = 2 * atan(b / a);
      common = 200 / (theta * k + a);
      l = a * common;
      w = b * common;
      printf("Case %d: %.10lf %.10lf\n", test, l, w);
      test++;

    }
    return 0;
  }

 

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