Respuesta:
[tex]6m[/tex]
Explicación paso a paso:
Por Pitágoras.
[tex](CD)^{2} =(ED)^{2} +(EC)^{2}[/tex]
[tex]10^{2} = 6^{2} +(EC)^{2}[/tex]
[tex]10^{2} -6^{2} = (EC)^{2}[/tex]
[tex]100-36 = (EC)^{2}[/tex]
[tex]64 = (EC)^{2}[/tex]
[tex]EC = \sqrt{64}[/tex]
[tex]EC = 8m[/tex]
Aplicando proporcionalidad:
[tex]\frac{AB}{BF} =\frac{BC}{EB}[/tex]
[tex]\frac{AF+BF}{BF} = \frac{EC+EB}{x}[/tex]
[tex]\frac{4m+3m}{3m} =\frac{8m+x}{x}[/tex]
[tex]x (4+3) = 3(8+x)[/tex]
[tex]x(7) = 24+3x[/tex]
[tex]7x = 24+3x[/tex]
[tex]7x-3x = 24[/tex]
[tex]4x = 24[/tex]
[tex]x = \frac{24}{4}[/tex]
[tex]Luego : x = 6m[/tex]
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Respuesta:
[tex]6m[/tex]
Explicación paso a paso:
Por Pitágoras.
[tex](CD)^{2} =(ED)^{2} +(EC)^{2}[/tex]
[tex]10^{2} = 6^{2} +(EC)^{2}[/tex]
[tex]10^{2} -6^{2} = (EC)^{2}[/tex]
[tex]100-36 = (EC)^{2}[/tex]
[tex]64 = (EC)^{2}[/tex]
[tex]EC = \sqrt{64}[/tex]
[tex]EC = 8m[/tex]
Aplicando proporcionalidad:
[tex]\frac{AB}{BF} =\frac{BC}{EB}[/tex]
[tex]\frac{AF+BF}{BF} = \frac{EC+EB}{x}[/tex]
[tex]\frac{4m+3m}{3m} =\frac{8m+x}{x}[/tex]
[tex]x (4+3) = 3(8+x)[/tex]
[tex]x(7) = 24+3x[/tex]
[tex]7x = 24+3x[/tex]
[tex]7x-3x = 24[/tex]
[tex]4x = 24[/tex]
[tex]x = \frac{24}{4}[/tex]
[tex]Luego : x = 6m[/tex]