To find the length of the diagonal of a square garden, we first need to know the relationship between the area and the side length of the square. The area (A) of a square is given by the formula:
A = side²
In this case, the area is 200 m². We can calculate the length of one side of the garden:
side = √A = √200 m²
This simplifies to:
side ≈ 14.14 m
Now, to find the length of the diagonal (d) of the square, we can use the formula:
d = side × √2
Substituting the side length we found:
d ≈ 14.14 m × √2 ≈ 14.14 m × 1.414 ≈ 20 m
So, the length of the diagonal of the square garden is approximately 20 meters.