When a diagonal is drawn into a square, the shape takes on the properties of other geometric figures. A diagonal is an interior line segment within a polygon that connects opposite corners or vertices. The diagonal of a square bisects it, and converts it into two isosceles right triangles with the diagonal as the hypotenuse of each triangle. Given the triangular properties of a square's diagonal, you can find the length of a square's side using the Pythagorean theorem, where the square of the length of the hypotenuse equals the squared length of each side, added together.
Instructions
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1
Measure the length of one of the diagonals. Square the measurement. For example, let the diagonal measure 4 inches. Four inches multiplied to itself results in 16 square inches.
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2
Divide the squared amount in half: 16 square inches divided by 2 equals 8 inches.
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3
Calculate the half's square root. Concluding the example, the square root of 8 is 2√2 or approximately 2.828 inches. The length of one side of the square is 2.828 inches.