Perimeter of a flat figure call the sum of lengths of all its parties. But to find the parties of a figure, knowing only perimeter - not always a feasible task. Often additional data are required.
Instruction
1. For a square or a rhombus a task to find the parties from perimeter decides it is very simple. It is known that at these two figures on 4 sides and all of them are equal among themselves therefore the perimeter of p of a square and rhombus is equal 4a where an is the party of a square or rhombus. Then length of the party is equal one fourth perimeters: = p/4.
2. This task and for an equilateral triangle is easily solvable. At it three party, identical on length, therefore the perimeter of p of an equilateral triangle is equal 3a. Then party of an equilateral triangle of a = p/3.
3. Additional data will be necessary for other figures. For example, it is possible to find the parties of a rectangle, knowing its perimeter and the area. Let's assume that length of two opposite parties of a rectangle is equal a, and length of two other parties - b. Then the perimeter of p of a rectangle is equal to 2 (a+b), and the area of s is equal to ab. Let's receive the system of the equations with two unknown: p = 2 (a+b) of s = ab. Let's express from the first equation and: and = p/2 - b. Let's substitute in the second equation and we will find b: s = pb/2 - b². A discriminant of this equation of D = p²/4 - 4s. Then b = (p/2±D^1/2)/2. Reject that root which will be less than zero, and substitute in expression for the party of a.