The side length of the square garden bed is 2/3 and the side length of the triangular garden bed is 3.
The two garden beds shown in the image have equal perimeters.
This means that the total length of all the sides of the square garden bed is the same as the total length of all the sides of the triangular garden bed.
To write an equation that sets the perimeters equal, we need to know the formulas for the perimeters of a square and a triangle.
The perimeter of a square is equal to the length of one side times 4.
The perimeter of a triangle is equal to the sum of the lengths of all three sides.
Using these formulas, we can write the following equation:
4x = x + 1 + 2x + 1
Where x is the side length of the square garden bed.
Combining like terms, we get:
3x = 2
Dividing both sides by 3, we get:
x = \frac{2}{3}
Therefore, the side length of the square garden bed is 2/3.
To find the side length of the triangular garden bed, we can substitute x = 2/3 into the equation for the perimeter of the triangle.
Perimeter = x + 1 + 2x + 1
Perimeter = \frac{2}{3} + 1 + \frac{4}{3} + 1
Perimeter = \frac{9}{3}
Therefore, the side length of the triangular garden bed is 3.
Answer to part b:
The side length of a garden cannot be a negative number or zero. Therefore, the only value of x that makes the equation 4x = x + 1 + 2x + 1 true in the context of this problem is x = 2/3.