The area of a square garden is 200 m². How long is the diagonal? step by step

Answer 1

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.