Answer: the length of the smallest side is 11 feet.
the length of the medium side is 27 feet.
the length of the longest side is 28 feet.
Step-by-step explanation:
Let x represent the length of the smallest side.
Let y represent the length of the middle side.
Let z represent the length of the longest side.
The perimeter of a triangular garden is 66 feet. This means that
x + y + z = 66 - - - - - - - - - -1
if the middle length side is 5 feet greater than twice the length of the smallest side, it means that
y = 2x + 5
The longest side is 5 feet less than 3 times the length of the smallest side. It means that
z = 3x - 5
Substituting y = 2x + 5 and z = 3x - 5 into equation 1, it becomes
x + 2x + 5 + 3x - 5 = 66
6x = 66
x = 66/6 = 11
y = 2x + 5 = 2 × 11 + 5
y = 27
z = 3x - 5 = 3 × 11 - 5
z = 28
