The first side of a triangle is twice the length of the second side; the third side is 20 feet less than three times the second side. the perimeter of the triangle is 106 feet. find the three sides.

Let the second side be x

then,
first side = twice the length of the second side
= 2x

third side = 20 feet less than three times the second side
3 (second side ) - 20
= 3 (2x) -20
= 6x - 20

perimete of a triangle = sum of all sides,

substitute the values we know,
and you'll be left with this equation

106 = x + 2x + 6x - 20
106+ 20 = 9x
126 = 9x
126/9 = x
14 = x

so,

measure of second side = x = 14 feet

measure of first side = 2x = 2 (14) = 28 feet

measure of thurd side = 6x - 20 = 6 (14)-20 = 84- 20 = 64 feet.