Finding the Length of Each Side of a Square Given its Diagonal
Understanding the relationship between the diagonal and the side of a square is crucial in geometry. In this article, we will delve into a detailed explanation of how to calculate the side length of a square when the diagonal is known. This involves the application of the Pythagorean theorem, a fundamental concept in geometry.
Introduction to the Problem
Suppose the diagonal of a square measures (7sqrt{2}) units. How can we determine the length of each side of the square? Let's explore the solution step by step.
Using the Pythagorean Theorem
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In the context of a square, the diagonal serves as the hypotenuse of the right-angled triangles formed by the sides of the square.
Let the side length of the square be s. According to the Pythagorean theorem, the relationship between the side length and the diagonal d can be expressed as: d2 s2 s2 This simplifies to d2 2s2.Applying the Given Information
We are given that the diagonal d is 7√2. Substitute this value into the equation:72 × 2 2s2
Calculate: 72 49 49 × 2 98 Therefore, 2s2 98.Solving for the Side Length
Divide both sides by 2: s2 49 Take the square root of both sides: s √49 7 unitsHence, the length of each side of the square is 7 units.
Conclusion
By using the Pythagorean theorem, we have successfully determined the length of each side of a square given its diagonal. The key steps include understanding the relationship between the diagonal and the sides of the square, applying the Pythagorean theorem, and solving for the unknown side length.
Keywords: square diagonal, side length, Pythagorean theorem