You will need

- - Pythagorean theorem;
- the ratio of sides and angles of a right triangle;
- calculator.

Instruction

1

Because

**square**diagonals are equal (the property that he inherited a "legacy" of the rectangle), in order to find**side****of a square**is enough to know the length of one diagonal. Diagonal and two sides**of the square**adjacent to it, imagine a rectangular (because all the angles**of the square**are straight) and isosceles (since all sides of this figure are equal) triangle. In this triangle the sides**of the square**are the legs, and*diagonal is*the hypotenuse. To find**side****of a square**, use the Pythagorean theorem.2

Since the sum of the squares of the other two sides that are equal to a, is equal to the square of the hypotenuse, which indicate c (c2=a2+a2), the leg will be equal to the hypotenuse divided by the square root of the number 2, and what comes of the preceding expression a=c/√2. For example, to find

**the side****of a square**with*diagonal*12 Yu cm, this number divide by the square root of 2. Get a=12/√2≈8.5 cm given the fact that the square root of 2 is not removed, all the answers will have to round to the required accuracy.3

Side

**of the square**find using the ratio of sides and angles in a right triangle that forms*the diagonal of*u and the adjacent sides. It is known that one of the corners of the triangle a straight line (as the angle between the sides**of the square**) and the other two are equal and amount to 45°. This property stems from ravnoudalennostj of this triangle, since the sides of it are equal.4

To find

**side****of a square**, multiply the*diagonal*by the sine or the cosine of the angle of 45 ° (they are equal to each other as the adjacent and opposite sides, sin(45º)=cos(45°)=√2/2) a=c∙√2/2. For example, given a*diagonal***of a square**is 20 cm, find the**side**. Make the calculation according to the above formula, the result will be a side**of a square**with the desired degree of accuracy a=20∙√2/2≈14,142 see