What happens to the perimeter when the length of a rectangle is shortened?
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Denote length,width and perimeter by $ (x,y,P) $ respectively. Show
Solving the two simultaneous equations $$ x+y=P, \quad 0.9 x + 0.8 y = 0.88 P, $$ you get $$x= 0.8 P, \quad y= 0.2 P $$ Plugging into the new perimeter $$ 0.8 \,* \, 0.8 P + 0.9 \,*\, 0.2 P =0.82 P. \, $$ That makes $ 100-82= 18$ % reduction in perimeter. The perimeter of a two-dimensional shape is the total length of the outline. To find the perimeter of a rectangle, we add the lengths of all four sides. Since opposite sides of a rectangle are always equal, we need to find the dimensions of length and width to find the perimeter of a rectangle. We can write the perimeter of the rectangle as twice the sum of its length and width. The perimeter is a linear measure and has units as meters, centimeters, inches, feet, etc. Formula for the Perimeter of a RectangleThe letter ‘P’ denotes the perimeter of a rectangle. Let l denote the length and w denote the width of the rectangle. The perimeter (P) of a rectangle is the total length of all the sides of the rectangle. Since the opposite sides of a rectangle are equal, a rectangle has two equal lengths and two equal widths. The formula for the perimeter of a rectangle is given below: Perimeter = length + length + width + width P = l + l + w + w Or, P = 2 (l + w) Hence, the formula for the perimeter of a rectangle, P = 2 × (length + width) = 2 × (sum of adjacent sides) Real-World Applications
Solved Examples
Solution: Length of the rectangle, l = 25 cm Width of the rectangle, w = 4 cm Perimeter of the rectangle, P = 2 (l + w) = 2 (25 + 4) = 58 The perimeter of the given rectangle is 58 cm.
Solution: The length of the rectangular yard is 10 m more than the width. Since the length of the yard is 25 m, the width of this rectangular yard is 25 m – 10 m or 15 m. Length of the yard, l = 25 m Width of the yard, w = 15 m Perimeter, P = 2 (l + w) = 2 (25 + 15) = 2 (40) = 80 The perimeter of the given rectangle is 80 m.
Solution: Using the formula P = 2 (l + w), we can say that 2 (35 + w) = 100 Or, 35 + w = 1002 = 50 Therefore w = 50 – 35 = 15 The width of the given rectangle is 15 cm. Practice ProblemsPerimeter Of A RectangleAttend this Quiz & Test your knowledge. 1 40 cm 45 cm 50 cm 55 cm CorrectIncorrect Correct answer is: 55 cm 2 100 cm 110 cm 115 cm 120 cm CorrectIncorrect Correct answer is: 120 cm 3 135 cm 170 cm 200 cm 270 cm CorrectIncorrect Correct answer is: 270 cm 4 60 cm 75 cm 100 cm 150 cm CorrectIncorrect Correct answer is: 75 cm Frequently Asked QuestionsWhat is the difference between the perimeter and area of a rectangle? The perimeter measures the length of the boundary of the rectangle. It is given by the sum of all sides of the rectangle and expressed in linear units. Area, on the other hand, measures the space within the rectangle. It is the product of the length and width of the rectangle and is expressed in square units. Which unit of measurement is used to measure the perimeter of a rectangle? Since the perimeter of a rectangle is the total distance covered by its boundaries or the sides, the unit of the perimeter (as distance) can be centimeters, meters, feet, yards, etc. Can rectangles with the same perimeters have different sides and areas?  Source How can you find the length of a rectangle with the given width and perimeter? Perimeter of Rectangle = 2 (Length + Width). Rearranging the terms in this formula, we get, Length = $\frac{Perimeter}{2}$ – Width. So, to find the length of a rectangle, subtract the width from half of the perimeter. How does perimeter relate to length?What is Perimeter? In geometry, the perimeter of a shape is defined as the total length of its boundary. The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape. It is measured in linear units of measurement like centimeters, meters, inches, or feet.
How is the perimeter of a rectangle related to its length and width?Find the perimeter of a rectangle if its length is 6 cm and breadth is 4 cm. We know that, perimeter of a rectangle = 2 (Length + Breadth) units. Hence, the perimeter of a rectangle is 20 cm, if its length equals 6cm and breadth equals 4 cm.
What happens to the perimeter of a square if the length of each side is tripled?Let the first square have sides of length x meter. If sides get tripled, then the side of the new square will be 3 times the earlier side. We know that the formula of the perimeter of the square is 4×side. Therefore, the perimeter of the new square is 3 times the perimeter of the first square.
What will happen to the perimeter of a rectangle if its length is doubled and breadth remains?Therefore, the new perimeter is double the original one. Q.
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