In mathematics, a rectangle is considered a quadrilateral geometric shape, in which every two opposite sides are parallel and equal in length, and all
An overview of the perimeter of a rectangle
In mathematics, a rectangle is considered a quadrilateral geometric shape, in which every two opposite sides are parallel and equal in length, and all of its angles are right; That is, the measure of each of the angles of the rectangle is equal to ninety degrees, and the sides of the rectangle are called length and width, and it should be noted that the square is a special case of the rectangle. Where the length in it is equal to the width.
The perimeter is generally known as the amount of the outside distance that surrounds the geometric shape, in other words, the perimeter is the length of the line that surrounds the two-dimensional shape, such as: a circle, rectangle, or square, and in the case of a rectangle, it can be said simply that the perimeter of the rectangle is the sum of the lengths of its sides.
The law of the perimeter of a rectangle
The perimeter of a rectangle can be calculated in several ways as follows:
- When you know its length and width:
- The perimeter of the rectangle = the length of the first side + the length of the second side + the length of the third side + the length of the fourth side , and because every two opposite sides in the rectangle are equal in length, the formula can be written as follows: the perimeter of the rectangle = 2 x length + 2 x width , and in symbols: H = 2 x A + 2 x B , where:
- A: The length of the rectangle.
- B: The width of the rectangle.
- When you know the area and length, or area and width :
- The perimeter of the rectangle = (2 x the area of the rectangle + 2 x the square of the length or the square of the width) / the length or width , and in symbols: h = ((2 x m + 2 x a²) / a or h = ((2 x m + 2 x b²) ) / B ; where:
+ H: the perimeter of a rectangle.
+ M: area of a rectangle.
+ A: The length of the rectangle.
+ B: The width of the rectangle.
+ M: area of a rectangle.
+ A: The length of the rectangle.
+ B: The width of the rectangle.
- When you know the length of the diagonal and the length, or the length of the diagonal and the width :
- The perimeter of a rectangle = 2 x (length or width + (diagonal square - height square or width square) √) , and in symbols: h = 2 x (a + (s²-a²) √) , or h = 2 x (b + (s²) -B²) √) ; Where:
+ B: The width of the rectangle.
+ S: the length of the diameter of the rectangle.
+ H: the perimeter of a rectangle.
Examples of calculating the perimeter of a rectangle
- The first example: Calculate the perimeter of a rectangle, if it is known that its length is 6 cm, and its width is 3 cm.
- The solution: Using the formula for the perimeter of a rectangle = 2 x length + 2 x width, it is obtained that the perimeter of the rectangle = 2 (6) +2 (3) = 18 cm.
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- The second example: The soccer coach ordered Sami to run around the field 3 turns, and the field was rectangular, 160 meters long and 53 meters wide. Find the total distance that player Sami would run around the field.
- The solution:
+ Since Sami will run around a rectangular court, the distance that he will travel will be equal to the circumference of this rectangle, which can be calculated by substituting the length and width of the playing field into the rule of the circumference of the rectangle, as follows:
+ The perimeter of the playing field = (2 x 160) + (2 x 53) = 426 m
+ Since Sami will run 3 laps, then he will run a distance equal to three times the circumference of the stadium, and for this: Total running distance = 426 x 3 = 1278 m
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- Third example : Calculate the perimeter of a rectangle that is 7.5 cm long and 4.5 cm wide.
- Substituting the numbers into the formula for the perimeter of the rectangle results that: The perimeter of the rectangle = 2 x length + 2 x width = 2 x 7.5 + 2 x 4.5 = 24 cm.
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- Fourth example : Find the length of a rectangle if its circumference is 18 cm and its width is 5 cm.
- The solution:
+ Using the general formula of the perimeter of a rectangle, it is obtained that: The perimeter of the rectangle = (2 x length) + (2 x width). 36 = (2 x length) + (2 x 10),
+ and by solving the equation, it turns out that: Length = 8 cm._________________________________________________________________________________
- Fifth example : A rectangle whose length is 7 units and width is 4 units. Find its perimeter.
- The solution:
+ Using the law of the perimeter of a rectangle, the calculation of the circumference for it is as follows:
+ The perimeter of the rectangle = (2 x length) + (2 x width) = 2 x 7 + 2 x 4 = 22 units.
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- Sixth example: a rectangular circumference is equal to 14 m, and its width is 4 m. Find its length.
- The solution:
+ Using the general formula of the perimeter of a rectangle, it is obtained that: The perimeter of the rectangle = (2 x length) + (2 x width). 14 = (2 x length) + (2 x 4),
+ and by solving the equation, it turns out that: Length = 3 m._________________________________________________________________________________
- The seventh example: If the area of a rectangle is 96 cm² and its width is 4 cm less than its length, find its perimeter.
- The solution:
+ In this question, the length can be expressed with the value a, and the width as (a-4), and since the area of the rectangle = length x width, then: 96 = a (a-4), and of it 96 = a-squared-4a, and by solving the quadratic equation and excluding the value The negative results in: A = 12 cm.
+ Using the formula: H = ((2 x M + 2 x A²) / A, and substituting the values in it results in: H = ((2 x 96 + 2 x 12²) / 12 = 40 cm.
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- Example 8: If the area of a rectangle is 56 square meters and its width is 4 meters, find its perimeter.
- The solution:
+ Using the formula: H = ((2 x M + 2 x A²) / A, and substituting the values in it results in: H = ((2 x 56 + 2 x 4²) / 4 = 36 cm.
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- Example 9: If the width of a rectangular field is 30 meters, and its length is less than three times the width of the field by 10 meters, find its perimeter.
- The solution:
+ In this example, the width = 30 m, while the length equals: length = 3 x width -10 = 3 x 30 - 10 = 80 m, and using the general rule of the perimeter of the rectangle, it turns out that: the perimeter of the rectangle = (2 x 80) + (2 x 30) = 160 + 60 = 220 m.
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- Example 10: Find the perimeter of a rectangle if it is 40 cm long and 41 cm in diameter.
- The solution:
+ Using the formula: h = 2 x (a + (s²-a²) √), it turns out that: H = 2 x (40+ (41²-40²) √) = 2 x 49 = 98 cm.
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- Example Eleven: If the perimeter of a rectangle is 102 cm, and the diameter is 39 cm, find its dimensions.
- The solution:
- + Using the formula: h = 2 x (a + (s²-a²) √), it turns out that: 102 = 2 x (a + (39²-a²) √), 51-a = (1521-a²) √, and by square both sides: (51-a) ² = 1521-a², and by simplifying the terms, it turns out that: A²-51a + 540 = 0, and by solving the quadratic equation it comes out that: A = 15 cm, or 36 cm
+ Substitute in the general formula for the circumference of the rectangle = 2 x length + 2 x width, to result in:
+ If A = 15, then: 102 = 2 x 15 + 2 x width, and of that the width = 36 cm.
+ If A = 36, then: 102 = 2 x 36 + 2 x width, and of that the width = 15 cm.
+ That is, the dimensions of the rectangle = 15 cm, 36 cm.
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