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Post a LessonAnswered on 22/02/2024 Learn CBSE - Class 6/Maths/Mensuration/Perimeter and area
Sadika
The perimeter of a closed figure is the total length of the boundary or outer edge of the figure. In other words, it is the distance around the entire shape. For polygons, such as rectangles, squares, triangles, and irregular shapes, the perimeter is calculated by adding together the lengths of all the sides of the figure. The unit of measurement for perimeter is typically the same as the unit of measurement used for the sides of the figure (e.g., centimeters, meters, inches, etc.). The perimeter is a measure of the outline or boundary of the figure and is often used to determine the amount of fencing needed for enclosing an area or the distance around a property.
Answered on 22/02/2024 Learn CBSE - Class 6/Maths/Mensuration/Perimeter and area
Sadika
To find out how many rectangles can be formed by folding a wire of length 20 meters into a rectangle with sides as positive integers in meters, we can start by considering the possible combinations of side lengths.
Let's denote the length of one side of the rectangle as xx meters and the length of the other side as yy meters. Since the wire has a length of 20 meters, the perimeter of the rectangle formed by folding the wire must be equal to 20 meters. Therefore, we have the equation:
2x+2y=202x+2y=20
Simplifying this equation, we get:
x+y=10x+y=10
Now, we need to find pairs of positive integers xx and yy that satisfy this equation and represent the possible side lengths of the rectangle.
The pairs of positive integers xx and yy that satisfy x+y=10x+y=10 are: (1,9),(2,8),(3,7),(4,6),(5,5),(6,4),(7,3),(8,2),(9,1)(1,9),(2,8),(3,7),(4,6),(5,5),(6,4),(7,3),(8,2),(9,1)
Each of these pairs represents a unique rectangle. However, notice that for each pair (x,y)(x,y), we also have the pair (y,x)(y,x), which represents the same rectangle but with the sides swapped. Since the order of the sides doesn't matter for a rectangle, we can cut the number of distinct rectangles in half by considering only one of the pairs for each unique combination of side lengths.
Therefore, the total number of distinct rectangles that can be formed by folding the wire into a rectangle with sides as positive integers is half the number of pairs, which is 92=4.529=4.5.
However, since we cannot have half a rectangle, we need to consider only the integer part of 4.5, which is 4.
So, 4 rectangles can be formed by folding the wire if the sides are positive integers in meters.
Answered on 22/02/2024 Learn CBSE - Class 6/Maths/Mensuration/Perimeter and area
Sadika
To find the length of the wire needed to fence a square piece of land with each side equal to 100 meters and using 3 layers of metal wire, we need to calculate the total length of wire required to enclose the perimeter of the square.
Since the land is square, all four sides are equal in length. Therefore, the perimeter PP of the square can be calculated by multiplying the length of one side ss by 4:
P=4×sP=4×s
Given that each side of the square is 100 meters, we have:
P=4×100P=4×100 P=400P=400
This gives us the total perimeter of the square land, which is 400 meters.
Since we are using 3 layers of metal wire, we need to multiply the perimeter by 3 to account for each layer:
Total length of wire=3×PTotal length of wire=3×P Total length of wire=3×400Total length of wire=3×400 Total length of wire=1200Total length of wire=1200
Therefore, the total length of wire needed to fence the square piece of land with each side equal to 100 meters and using 3 layers of metal wire is 1200 meters.
Answered on 22/02/2024 Learn CBSE - Class 6/Maths/Mensuration/Perimeter and area
Sadika
To determine who covers the smaller distance, we need to compare the perimeters of the square and the rectangle.
The perimeter of a square is calculated by multiplying the length of one side by 4. Given that the side of the square is 75 meters, the perimeter PsPs of the square is:
Ps=4×75=300 metersPs=4×75=300 meters
The perimeter of a rectangle is calculated by adding the lengths of all four sides. Given that the length of the rectangle is 60 meters and the breadth is 45 meters, the perimeter PrPr of the rectangle is:
Pr=2×(length+breadth)Pr=2×(length+breadth) Pr=2×(60+45)=2×105=210 metersPr=2×(60+45)=2×105=210 meters
Therefore, Shikha covers a distance of 300 meters around the square, while Priya covers a distance of 210 meters around the rectangle.
Since 210 meters is less than 300 meters, Priya covers the smaller distance.
Answered on 22/02/2024 Learn CBSE - Class 6/Maths/Mensuration/Perimeter and area
Sadika
To find the length of the wooden frame needed to frame the picture, we need to calculate the perimeter of the photograph, which will give us the total length of the frame required.
The perimeter PP of a rectangle is calculated by adding the lengths of all four sides. Given that the dimensions of the photograph are 30 cm by 20 cm, the perimeter PP is:
P=2×(length+breadth)P=2×(length+breadth) P=2×(30 cm+20 cm)P=2×(30 cm+20 cm) P=2×50 cmP=2×50 cm P=100 cmP=100 cm
This gives us the total perimeter of the photograph, which is 100 cm.
Since the wooden frame will be placed around the entire perimeter of the photograph, the length of the wooden frame needed will be the same as the perimeter of the photograph.
Therefore, the length of the wooden frame needed to frame the picture is 100 cm.
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