The perimeter of a triangular garden is 78 feet. Find the length of the three sides if the middle length side is 3 feet greater than twice the length of the smallest side, and the longest side is 3 feet less than 3 times the length of the smallest side.

36, 29 and 13

Step-by-step 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

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step-by-step explanation: