A wire is in the shape of a square of side 10cm. If the wire is rebent in to a rectangle of length 12cm.find its breadth which figure encloses more area and by how much.
Length of wire:
Perimeter of square = 4*side = 4*10 = 40cm
Original area:
Area of square = (side)^2 = (10cm)^2 = 100cm^2
Dimensions of rectangle:
Perimeter = 2(l + b) = 40cm (Since the length of wire is the same)
=> 2(l + b) = 40
=> l + b = 20
If l is 12, b is 8
Area of rectangle:
Area = Length*Breadth = 12*8 = 96 cm^2
Which area is more?
What is the difference?
To find out which figure encloses more area and by how much, we can calculate the areas of both the square and the rectangle.
1. Area of the square:
The side length of the square is given as 10 cm, so the area of the square is calculated by squaring the side length:
Area of the square = side length * side length = 10 cm * 10 cm = 100 cm^2
2. Area of the rectangle:
The length of the rectangle is given as 12 cm, and the width (breadth) is what we need to find. Since the wire is rebent into the rectangle, the total length of the wire remains the same, which is the perimeter of the square. The perimeter of a square can be calculated by multiplying the side length by 4:
Perimeter of the square = 4 * 10 cm = 40 cm
Since the wire is rebent into the rectangle, the perimeter of the square is equal to the total length of the wire. Therefore, the perimeter of the rectangle is also 40 cm.
Now, we can calculate the width (breadth) of the rectangle using the perimeter and length:
Perimeter of the rectangle = 2 * (length + breadth)
40 cm = 2 * (12 cm + breadth)
20 cm = 12 cm + breadth
breadth = 20 cm - 12 cm
breadth = 8 cm
Now, we can calculate the area of the rectangle:
Area of the rectangle = length * breadth = 12 cm * 8 cm = 96 cm^2
Comparing the areas:
Area of the square = 100 cm^2
Area of the rectangle = 96 cm^2
Therefore, the square encloses more area than the rectangle by 4 cm^2 (100 cm^2 - 96 cm^2).