Often in life people need to find the perimeter of a rectangle.This problem occurs, for example, in cases where you need to calculate the length of the fence or the amount of wallpaper needed for pasting the walls in the room.However, in the latter case, the perimeter is only an intermediary solve practical problems.But nevertheless, in this case, people also need to know how to find the perimeter of the rectangle.
To begin with I would like to define what is the perimeter.Perimeter, in fact, the boundary of a particular geometric shape, or the total length of its borders.Now, explain the meaning of the rectangle.Parallelogram with right angles should be classified as rectangles.Actually, the main feature are precisely its angles, which must be in the geometric figure four.
Thus, to find the total length of the boundary of the rectangle, you must add up the lengths of all its sides.As we have seen, the parallel sides of the rectangle are equal, therefore, to facilitate understanding, it should be understood that the perimeter of a rectangle is equal to twice the sum of its two sides.
For clarity denote equal sides in a rectangle in the Latin alphabet "a" and «b», respectively.Thus, it appears that P (perimeter of a rectangle) = a + b + a + b.This equation can be transformed into the following formula: P = 2 × (a + b).
However, in reality there are often situations where the known length of only one hand and some other parts in the box, or outside it.Consider a few options.
For example, we need to figure out what is the perimeter of a rectangle, provided that the length of one side of the rectangle is unknown, but is known for its area.It is necessary, using the formula for calculating the area of a rectangle, which is the product of its sides, to calculate the length of its second side.This is easily done by dividing a certain area at a certain direction.Knowing both sides in the rectangle can be easily calculated and its perimeter.
This option is suitable for calculating the required amount of material for the fence portion when an area is listed in the documentation.It is necessary to further measure one side of the plot.But sometimes you need to know how to find the perimeter of a rectangle if we know one of the sides of the rectangle and the diagonal.
Naturally, the first step in the calculation is to find the length of the second side of the rectangle.It can be calculated by the Pythagorean theorem, which states that the hypotenuse of a right triangle, erected in the square, includes the sum of the squares of the two sides.Therefore, we need to calculate the length of erect diagonal length and a certain aspect squared, then finding the difference between them, and from this difference has to be to take the square root.
obtained the square root will be the length of an unknown side.And how to find the perimeter of a rectangle can be folded known lengths of the sides and their doubling, each with the process can easily handle.
In mathematics lessons are also considering how to find the perimeter of a rectangle on its diagonal and one acute angle formed by the diagonal and one side of the rectangle.Here we have a classic example of the use in the calculation of the sine.Because the curriculum is well known that the sine of the angle of a right triangle equals the ratio of the adjacent side and the hypotenuse.Hence the formula: sin x = leg: the hypotenuse (the diagonal of the rectangle).
Sinus can be easily found on the table Bradis, substituted into the formula known value of the diagonal - the hypotenuse, and easily calculated one side of the rectangle.Now the next step is finding a second side of the rectangle.It comes into force discussed above variant using Theorem Pifogora.Squaring known diagonal and deducted from the square of the number of parties found.From the response of square roots.By now known sides can calculate the perimeter, their length and folded double.
Naturally, this option is not exhaustive examples, in fact, there are many more, but the above are the most common.
Thus, we can conclude that, without knowledge of the lengths of the two parallel sides of the rectangle define the perimeter is practically impossible.However, using an arsenal of geometric theorems and axioms, you can always find the perimeter of a rectangle, folded with all its sides.
