Answer:
3, 6 and 8
Step-by-step explanation:
In order to solve the problem, we call:
[tex]a[/tex] = length of the 1st side of the triangle
[tex]b[/tex] = length of the 2nd side of the triangle
[tex]c[/tex] = length of the 3rd side of the triangle
From the text of the question, we know that:
- One side of a triangle is twice the shortest side --> we can write this as
[tex]b=2a[/tex] (1) (assuming "a" is the shortest side)
- The third side is five feet more than the shortest side. -->
[tex]c=a+5[/tex] (2)
- The perimeter is 17 feet -->
[tex]a+b+c=17[/tex] (3)
So now we have 3 equations with 3 unknown variables. Substituting (1) and (2) into (3) we can find the value of "a", the shortest side:
[tex]a+2a+a+5=17\\4a=17-5=12\\a=3[/tex]
And so
[tex]b=2\cdot 3=6\\c=3+5=8[/tex]
So the lengths of the 3 sides are 3, 6 and 8.
