Answer:
36, 29 and 13
Explanation:
Let 'a' be the longest side.
Let 'b' be the middle side.
Let 'c' be the smallest side.
From the question given above,
The perimeter of a triangular garden is 78 feet. This can be written as:
Perimeter = a + b + c
78 = a + b + c ...... (1)
The middle length side is 3 feet greater than twice the length of the smallest side. This can be written as follow:
b = 2c + 3 ...... (2)
The longest side is 3 feet less than 3 times the length of the smallest side. This can be written as follow:
a = 3c – 3 ..... (3)
Summary:
78 = a + b + c ...... (1)
b = 2c + 3 ...... (2)
a = 3c – 3 ..... (3)
Substitute the value of a in equation
3 and the value of b in equation 2 into equation 1
78 = a + b + c
b = 2c + 3
a = 3c – 3
78 = (3c – 3) + (2c + 3) + c
78 = 3c – 3 + 2c + 3 + c
78 = 3c + 2c + c – 3 + 3
78 = 6c
Divide both side by 6
c = 78/6
c = 13
Substitute the value of c into equation 2 and 3 to obtain the value of b and a respectively
b = 2c + 3
c = 13
b = 2(13) + 3
b = 26 + 3
b = 29
a = 3c – 3
c = 13
a = 3(13) – 3
a = 39 – 3
a = 36
Therefore, the length of the three sides are: 36, 29 and 13