Final answer:
The dimensions of the triangular garden's sides are found using algebraic expressions. The shortest side is approximately 12.13 meters, the middle length side is approximately 30.33 meters, and the longest side is approximately 48.40 meters, based on the given relationships and perimeter.
Step-by-step explanation:
The perimeter of a triangular garden is 103m. To find the dimensions of each side, let's define the shortest side as x meters. The longest side is then 12 more than 3 times the shortest side, so it will be 3x + 12 meters. The middle lengthed side is five-halves the measurement of the shortest side, resulting in 5/2x meters. By adding these expressions together, we can set up the equation for the perimeter: x + (3x + 12) + (5/2x) = 103.
Combine like terms to solve for x:
- 1x + 3x + 5/2x = 103 - 12
- (5/2 + 4)x = 91
- (10/2 + 5/2)x = 91
- (15/2)x = 91
- x = 91 × (2/15)
- x = 12.1333...
The shortest side is approximately 12.13 meters. The middle length side is 5/2 times 12.13, yielding approximately 30.33 meters. The longest side, 3x + 12, is 3 times 12.13 plus 12, giving us approximately 48.40 meters.