Final answer:
To find the side lengths of the gardens, we set up an equation based on their perimeters. The side length of the square garden is found to be 15 meters, making the triangle's side 20 meters, as it's 5 meters longer. Therefore, the answer choice that closely matches these dimensions is missing from the options, suggesting a typo.
Step-by-step explanation:
The problem states that two gardens are being fenced in and they require the same amount of fencing, meaning both gardens have the same perimeter in meters. One garden is a square, and the other is an equilateral triangle. The length of each side of the triangle is 5 meters longer than each side of the square.
Let's denote the side length of the square as s. Therefore, each side of the equilateral triangle will be s + 5 meters. Because both gardens have the same perimeter, the perimeter of the square, which is 4s, must equal the perimeter of the triangle, which is 3(s + 5).
Setting these two expressions equal to each other gives us:
4s = 3(s + 5)
Solving for s we get:
4s = 3s + 15
s = 15
Therefore, the side of the square is 15 meters. The side of the triangle is 15 + 5 meters, which is 20 meters. So the correct answer is B. Square: 15m on each side, Triangle: 20m on each side, which isn't listed in the options provided, indicating a potential typo in the choices given.