Question

The perimeter of a triangular garden is 54 feet. Find the length of the three sides if the middle length side is 4feet greater than twice the length of the smallest​ side, and the longest side is 4feet less than 3 times the length of the smallest side.

Answer 1

Answer: 9 feet, 22 feet and 23 feet

Step-by-step explanation:

Let the smallest side be x.

The middle length side is 4feet greater than twice the length of the smallest​ side. This will be:

= (2 × x) + 4 = 2x + 4

The longest side is 4feet less than 3 times the length of the smallest side. This will be:

= (3 × x) - 4 = 3x - 4

Perimeter = x + 2x + 4 + 3x - 4

x + 2x + 4 + 3x - 4 = 54

Collect like terms

6x = 54

x = 54/6

x = 9

The three sides are

Smallest side = 9 feet

Middle side = 2x + 4 = 2(9) + 4 = 18+4 = 22 feet

Longest side = 3x - 4 = 3(9) - 4 = 27 - 4 = 23feet