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Hola:
A= √(S) (S-a) (S-b) (S-c)
S= (4 + 5 + 7)/2 = 16/2 = 8
S-a = 8- 4 = 4
S-b = 8-5 = 3
S-c = 8-7 = 1
A = √ (8) (4) (3) (1) = √96 = 9.7979
Si A = b x h/2
√96 = 7h/2 Sustitución.
2√96= 7h Despeje
2√96/7 = h
h = 2.799
En este procedimiento, me sale que la altura es 2.79
Espero te sea útil.