The area of a square garden is 200 m². How long is the diagonal? step by step
To find the length of the diagonal of a square garden, we can use the Pythagorean theorem.
Step 1: We know that the area of a square is given by the formula: Area = side length * side length = 200 m².
Step 2: Let's assume the side length of the square is represented by "x."
So, we have x * x = 200.
Step 3: Rearranging the equation, we get x² = 200.
Step 4: Taking the square root of both sides, we find x = √200.
Step 5: Simplifying √200, we get x ≈ 14.14.
Step 6: Since the diagonal of a square divides it into two right-angled triangles, we can use the Pythagorean theorem to find the length of the diagonal.
Let d represent the length of the diagonal.
Using the Pythagorean theorem, we have: d² = x² + x².
Substituting the value of x, we get d² = 14.14² + 14.14².
Simplifying, we find d² ≈ 398.
Step 7: Taking the square root of both sides, we find d ≈ √398.
Step 8: Evaluating √398, we find d ≈ 19.95.
Therefore, the length of the diagonal of the square garden is approximately 19.95 meters.