The diagonal of a square can be calculated using the formula: d = a√2, where 'd' represents the length of the diagonal and 'a' represents the length of a side of the square.
Here's a breakdown of how to find the diagonal:
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Understanding the Formula: The formula d = a√2 is derived from the Pythagorean theorem. A square's diagonal divides it into two right-angled triangles, where the diagonal is the hypotenuse and the sides of the square are the legs (a and b). Therefore, a² + a² = d², which simplifies to 2a² = d², and further to d = √(2a²) = a√2.
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Knowing the Side Length: To calculate the diagonal, you need to know the length of one side of the square ('a').
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Applying the Formula: Substitute the known side length ('a') into the formula d = a√2.
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Calculating the Result: Calculate the value of a√2. You can either use a calculator to find the approximate value of √2 (approximately 1.414) or leave the answer in radical form (e.g., 5√2).
Example:
Let's say a square has a side length of 5 cm. To find the diagonal:
- Formula: d = a√2
- Substitute: d = 5√2
- Calculate: d ≈ 5 * 1.414 ≈ 7.07 cm
Therefore, the diagonal of the square is approximately 7.07 cm. You could also express it as 5√2 cm.
In summary, to find the diagonal of a square, simply multiply the length of one of its sides by the square root of 2 (√2).
