Every year tasks in geometry become more difficult. The nobility is already not enough how to consider on ready formulas. It is necessary to be able from already ready to remove a new formula to learn any given size.
Instruction
1. Calculation of the parties of a square. A formula of the area of a square and², where and – the party of this figure. For calculation of the area of a square it is necessary to know only one party as all its parties are equal. From here it is very simple to calculate the party: a. Example: The area is equal to 49. Allocate a square root from 49. Answer: 7.
2. Calculation of the parties of a rectangle. To find the parties of this figure, knowing only value of the area, it is impossible. It is necessary to know one more size – its perimeter. Here an example, the area it is equal 12, and perimeter 14. Designate the parties of a rectangle "x" and "at". From a formula of calculation of perimeter P=2(a+b) substitute values of our task 2 (x + s) =14. From a formula of calculation of S=ab Square substitute values of our task hu =12, i.e. x =12/at. Substitute x value in the equation 2 (x + s) =14. It will turn out 2(12/y+ s) =14. Transfer similar 12/y+y=14/2. 12/at + at =7. Increase both members of equation on "at". It will turn out 12+ у^2=7у. – a quadratic equation, consider Ò^2-7Ò +12=0 through a discriminant. At the equation 2 roots at =4; at =3. Answer: the parties of a rectangle are equal to 3 and 4 cm respectively.
3. Calculation of the parties of a rhombus. To learn the parties of a rhombus (EWYP), besides the area it is necessary to have still some value. For example, height - WH, it is length of the perpendicular lowered from top (W) on the party (EP). It is necessary to remember that the parties of a rhombus are equal among themselves. In this case it is very easy to define the party of a rhombus (EW). It is known that the rhombus can be presented as two triangles of EWP and PWY, the area of each of which equals to a half of the work of height on the basis. It is possible to draw a conclusion that the area of a rhombus will be equal to the work of height at length of the party. From here the simple formula for calculation of length of the party rhombuses turns out: it is necessary to divide its square at height length - |EW| = S/|WH|. An example: Let the area of a rhombus of EWYP be equal to 20. And height WH=5. Substitute values in the given formula: |EW| =20/| 5. Answer: the party is equal to 4.
4. Calculation of the parties of an equilateral triangle. To learn its party (and all its parties are equal), besides the area it is necessary to know height. If two of these sizes are known, then calculation can be made on this formula: b=2S/h where b is the party of a triangle, S is the area, h is height. Example: Let the area of an equilateral triangle of ABC be equal to 25. BH height = 5. Substitute values in a formula: b=2*25/5. Answer: the party is equal to 10.