How to define the perimeter of a rectangle
The perimeter of any polygon - the sum of all the measurements of its sides. Challenges for the calculation of the perimeter of a rectangle occur in the course of the initial geometry. Sometimes you have found indirect evidence for their decision lengths of the sides. Check out the main types of tasks and methods of their solutions.
You will need:
- a pen; - Paper records.
Instruction how to define the perimeter of a rectangle
The perimeter of the rectangle, you can find folded lengths of all its sides. Since the opposing sides of the rectangle are equal, the perimeter can be defined by the formula: p = 2 (a + b), where a, b - the adjacent side.
EXAMPLE problems: in the condition it is said that one side of the rectangle has a length of 12 cm, and the second of its three times less. Required to find the perimeter.
To solve calculate the length of the second side: b = 12/3 = 4 cm. The perimeter of the rectangle will be: 2 (4 + 12) = 32 cm.
The third example - in the problem are only the length of one side and diagonal. The triangle formed by the two sides and the diagonal - square. Locate the second side of the equation of Pythagoras: b = (c ^ 2-a ^ 2) ^ 1/2. Then calculate the perimeter of the formula in Step 1.
The fourth example - given the length of the diagonal and the angle between the diagonal and the side of the rectangle. Calculate the length of the side of the expression: b = sina * c, where b - the opposed side corner of the rectangle, with - its diagonal. Find a corner adjacent to the side: a = cosa * c. Knowing the length of the sides, define the perimeter.
Fifth example - a rectangle inscribed in a circle with known radius. The circle center lies at the intersection of midperpendiculars polygon. For the rectangle is the same as the point of intersection of its diagonals. Hence, the length of the diagonal is equal to the diameter of a circle or two radii. Further, depending on the application conditions, get the sides of the polygon step is similar to 2 or 3.
Sixth example: what is the perimeter of a rectangle if its area - 32 cm2? It is also known that one of its sides is twice the other.
The area of the rectangle - it is the product of two adjacent sides. Label one side of the length of x. The second will be equal to 2. You have got an equation: 2x * x = 32. Solving it, get x = 4 cm Find a second side - 8 cm Calculate the perimeter:.. 2 (8 + 4) = 24 cm.