The perimeter of any polygon is the sum of measurements of all its parties. Tasks on calculation of perimeter of a rectangle meet in an initial course of geometry. Sometimes for them solutions of length of the parties need to be found according to indirect data. Get acquainted with the main types of tasks and methods of their decisions.
It is required to you
- - handle;
- - note paper.
Instruction
1. You can find rectangle perimeter, having put lengths of all its parties. As at a rectangle the opposite parties are equal, the perimeter can be set a formula: p = 2 (a+b) where and, b are the adjacent parties.
2. Example of a task: in a condition it is told that one party of a rectangle has length of 12 cm, and the second three times it less. It is required to find perimeter.
3. For the decision calculate length of the second party: b = 12/3 = 4 cm. The perimeter of a rectangle will be equal: 2(4+12) = 32 cm.
4. The third example – in a task only length of one party and diagonal are given. The triangle formed by two parties and diagonal – rectangular. Find the second party from Pythagoras's equation: b = (c^2-a^2) ^1/2. Then calculate perimeter on a formula from a step 1.
5. The fourth example – length of diagonal and a corner between the diagonal and the party of a rectangle is set. Calculate length of the party from expression: b = sina*c, where b – opposite to a corner the party of a rectangle, with – its diagonal. Find the party, adjacent to a corner: = cosa*c. Knowing lengths of the parties, define perimeter.
6. The fifth example – a rectangle is inscribed in a circle with the known radius. The center of a circle lies in a point of intersection of middle perpendiculars of a polygon. For a rectangle it coincides with a point of intersection of its diagonals. Means, length of diagonal is equal to diameter of a circle or two radiuses. Further, depending on statements of the problem, find the parties of a polygon similar to a step 2 or 3.
7. The sixth example: what is the rectangle perimeter equal to if its area – 32 cm2? It is known also that one its parties are twice more another.
8. The area of a rectangle is the work of two of its adjacent parties. Designate length of one party for x. The second will be equal the 2nd. At you the equation turned out: 2x*x = 32. Having solved it, find x = 4 cm. Find the second party – 8 cm. Calculate perimeter: 2(8+4) = 24 cm.