First we can set the equations we already know
[tex]a\text{ +b +c = 153 ft}[/tex]Where a, b and c are the sides of the triangle. Then, I will assign "a" the shortes side. One side is twice the shortest side so:
[tex]b\text{ = 2a }[/tex]Now, the sentence says, the third side is 17 feet longer that the shortes side "a":
[tex]c\text{ = a + 17}[/tex]Now we have a system of three equations with three unknown variables, so it will be easy to find the value of all the variables. If we put "b" and "c" in the first equation we have:
[tex]a\text{ + (2a) + (a+17) = 153 ft}[/tex][tex]\begin{gathered} 4a\text{ = 153-17} \\ 4a\text{ = }136 \\ a\text{ = 136/4} \\ a=34 \end{gathered}[/tex]Now, since we assigned "a" as the shortest side, we are done.
