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\( B A = 14 \)
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Para resolver este problema, primero observemos que \( C B + B D + D A = C A \). Dado que \( C B = 12 \), \( B D = 7 \) y \( D A = 7 \), sumamos estas longitudes: \[ C B + B D + D A = 12 + 7 + 7 = 26 \] Así que \( C A = 26 \). Si consideramos \( B A \) como parte de la distancia total \( C A \), podemos decir que: \[ C A = C B + B A + D A \] Esto nos lleva a \( 26 = 12 + B A + 7 \). Simplificando, tenemos: \[ 26 = 19 + B A \] Finalmente, restamos 19 de ambos lados para encontrar \( B A \): \[ B A = 26 - 19 = 7 \] Por lo tanto, \( B A = 7 \).
