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A wire is in the shape of a square if side 10cm .if the wire is rebent into a rectangle of length 12cm ,find its breadth which figure encloses more area and by how much
Verified Answer
A wire is in the shape of a square if side 10cm .if the wire is rebent...
Perimeter of square = perimeter of rectangle
4xside = 2(l+b)
4x10 = 2(12xb)
40 = 24b
b = 10/6
Area of the square
= sidexside
= 10x10
= 100 cm sq.
Area of the rectangle
= lxb
= 12 x (10/6)
= 20 cm sq
This question is part of UPSC exam. View all Class 7 courses
Most Upvoted Answer
A wire is in the shape of a square if side 10cm .if the wire is rebent...
According to the question,
Perimeter of square = Perimeter of rectangle
4 × side = 2 × ( l + b )
4 × 10 = 2 × ( 12 + b )
40 = 2 × ( 12 + b )
40/2 = 12 + b
20 = 12 + b
20 - 12 = b
6 = b
Area of Square = side² = 10² = 100 cm²
Area of Rectangle = l × b = 12 × 6 = 72 cm²
100 cm² > 72 cm²
Square > Rectangle
Thus, square encloses more area.
Perimeter of square = Perimeter of rectangle
4 × side = 2 × ( l + b )
4 × 10 = 2 × ( 12 + b )
40 = 2 × ( 12 + b )
40/2 = 12 + b
20 = 12 + b
20 - 12 = b
6 = b
Area of Square = side² = 10² = 100 cm²
Area of Rectangle = l × b = 12 × 6 = 72 cm²
100 cm² > 72 cm²
Square > Rectangle
Thus, square encloses more area.
Community Answer
A wire is in the shape of a square if side 10cm .if the wire is rebent...
Shape of the Wire:
The wire is initially in the shape of a square with a side length of 10 cm.
Rebending the Wire:
The wire is then rebent into a rectangle with a length of 12 cm. We need to find the breadth of this rectangle.
Calculating the Area of the Square:
The area of a square is given by the formula A = side^2.
For the given wire, the area of the square is A = 10^2 = 100 cm^2.
Calculating the Area of the Rectangle:
The area of a rectangle is given by the formula A = length * breadth.
Let's assume the breadth of the rectangle is 'b' cm.
Given that the length of the rectangle is 12 cm, the area of the rectangle is A = 12 * b = 12b cm^2.
Comparing the Areas:
To determine which figure encloses more area, we need to compare the areas of the square and the rectangle.
If the area of the square is greater than the area of the rectangle, then the square encloses more area.
If the area of the rectangle is greater than the area of the square, then the rectangle encloses more area.
Calculating the Difference in Area:
To find the difference in area between the square and the rectangle, we subtract the smaller area from the larger area.
If the square encloses more area:
Difference = Area of Square - Area of Rectangle = 100 cm^2 - 12b cm^2
If the rectangle encloses more area:
Difference = Area of Rectangle - Area of Square = 12b cm^2 - 100 cm^2
Conclusion:
To determine which figure encloses more area and the difference in area, we need to compare the values of the differences calculated above. The figure with the larger difference in area will enclose more area.
The wire is initially in the shape of a square with a side length of 10 cm.
Rebending the Wire:
The wire is then rebent into a rectangle with a length of 12 cm. We need to find the breadth of this rectangle.
Calculating the Area of the Square:
The area of a square is given by the formula A = side^2.
For the given wire, the area of the square is A = 10^2 = 100 cm^2.
Calculating the Area of the Rectangle:
The area of a rectangle is given by the formula A = length * breadth.
Let's assume the breadth of the rectangle is 'b' cm.
Given that the length of the rectangle is 12 cm, the area of the rectangle is A = 12 * b = 12b cm^2.
Comparing the Areas:
To determine which figure encloses more area, we need to compare the areas of the square and the rectangle.
If the area of the square is greater than the area of the rectangle, then the square encloses more area.
If the area of the rectangle is greater than the area of the square, then the rectangle encloses more area.
Calculating the Difference in Area:
To find the difference in area between the square and the rectangle, we subtract the smaller area from the larger area.
If the square encloses more area:
Difference = Area of Square - Area of Rectangle = 100 cm^2 - 12b cm^2
If the rectangle encloses more area:
Difference = Area of Rectangle - Area of Square = 12b cm^2 - 100 cm^2
Conclusion:
To determine which figure encloses more area and the difference in area, we need to compare the values of the differences calculated above. The figure with the larger difference in area will enclose more area.
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A wire is in the shape of a square if side 10cm .if the wire is rebent into a rectangle of length 12cm ,find its breadth which figure encloses more area and by how much Related: NCERT Solutions Chapter 11 (Part - 1) - Perimeter and Area, Maths, Class 7
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