Respuesta :
Let a, b, and c be the lengths of the sides (in ft) of the triangle.
Since one side of a triangle is twice the smallest side, the third side is four feet more than the shortest side and the perimeter is 12 feet, then f c is the length of the smallest side, then we can set the following system of equations:
[tex]\begin{gathered} a=2c, \\ b=c+4, \\ a+b+c=12. \end{gathered}[/tex]Substituting the first and second equations in the third one we get:
[tex]2c+c+4+c=12.[/tex]Adding like terms we get:
[tex]4c+4=12.[/tex]Subtracting 4 from the above equation we get:
[tex]\begin{gathered} 4c+4-4=12-4, \\ 4c=8. \end{gathered}[/tex]Dividing the above equation by 4 we get:
[tex]\begin{gathered} \frac{4c}{4}=\frac{8}{4}, \\ c=2. \end{gathered}[/tex]Finally, substituting c=2 in the first and second equations we get:
[tex]\begin{gathered} a=2\cdot2=4, \\ b=2+4=6. \end{gathered}[/tex]Answer: The lengths of all three sides (in feet) are: 2, 4, and 6.
