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Solution 1:
Apply cos c = (17^2 + 4^2 - 15^2)/2*17*4 = 10/17 in ADC.
In ABC, cos C = ( 17^2 + (4+x)^2 - 17^2) / 2*17*(4+x)
Find x.
Find the angle cos C, then take BD as x.
Then cos C will be same for both ADC and ABC
Apply in ABC and get x.
Solution 2:
x=BD.Then, 1156 + 289 * x= 225(x+4) + 4*x*(x+4) by Stewart's theorem => x = 16.
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