The triangle has 3 parties. The sum of lengths of these parties is also called perimeter. It is possible to find this indicator and without having all data. It is enough to learn simple rules.
It is required to you
- - Handle;
- - sheet of paper;
- - ruler;
- - pencil.
Instruction
1. The standard formula of finding of perimeter looks so: Р = a + b + with. In this formula and, b, c are lengths of each party of a triangle. This formula can be applied to any kind of triangles.
2. For example, if you have a triangle and its parties are equal 6 cm, 4 cm and 10 cm, then the perimeter will be calculated so: P=6+4+10=20 cm. Instead of these sizes, it is possible to put lengths of the parties, data in your task.
3. If you have a rectangular triangle and you know only sizes of two parties, then it does not become a big problem to find perimeter. It is enough to remember Pythagorean theorem in which it is said that the sum of squares of the parties adjacent to a corner of 90 degrees will be equal to a square of the party opposite to a right angle. The adjacent parties are called legs, and opposite — a hypotenuse. The hypotenuse will be as well the longest party of a rectangular triangle. Thanks to this formula it is possible to find any unknown party and then already to insert data and to calculate triangle perimeter.
4. For example, you gave a triangle which legs are equal to 3 and 4 cm. Then it turns out that the third party will be equal to a root from 25. Respectively the hypotenuse of such triangle will be equal to 5 cm, and the perimeter is equal to 12 cm.
5. If in a task lengths of two parties and a corner between them are given and it is necessary to find perimeter, but the triangle is not rectangular, then the theorem of cosines comes to the rescue. In it it is said that the square of the party will be equal to the sum of squares of two other parties minus a cosine of the angle lying between the known parties, increased by 2. As soon as the third party is found, with ease it is possible to find perimeter on a standard formula.
6. For example, if the parties are equal to 4 and 5 cm, and the corner between them is equal to 58 degrees, then the third party will be equal to root 16+25-2*0.529. It turns out, the unknown party is equal to a root from 39.942 and will be equal to 6.31 cm. And the perimeter of such triangle will be equal to 15.31 cm.