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A circular wire of diameter 42cm is folded in the shape of a rectangle whose sides are in the ratio 6:5. Find the ratio of the enclosed rectangle ?
- a)1080cm2
- b)1181cm2
- c)1250cm2
- d)1800cm2
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A circular wire of diameter 42cm is folded in the shape of a rectangle...
Radius = 42/2 = 21cm
Circumference = 2*22*21/7 = 132cm
L:b = 6x:5x
Perimeter of the rectangle = 2(6x+5x) = 22x
22x = 132
X = 6
Area = 6x * 5x = 30x*x
=30*6*6 = 1080cm2
Circumference = 2*22*21/7 = 132cm
L:b = 6x:5x
Perimeter of the rectangle = 2(6x+5x) = 22x
22x = 132
X = 6
Area = 6x * 5x = 30x*x
=30*6*6 = 1080cm2
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Community Answer
A circular wire of diameter 42cm is folded in the shape of a rectangle...
Understanding the Problem
To find the area of the rectangle formed by folding a circular wire, we start with the properties of the wire and the rectangle's dimensions.
Step 1: Calculate the Circumference of the Circle
- The diameter of the circle is 42 cm.
- The circumference (C) can be calculated using the formula: C = π * diameter.
- Thus, C = π * 42 cm ≈ 131.88 cm (using π ≈ 3.14).
Step 2: Determine the Rectangle's Dimensions
- The circumference of the circle becomes the perimeter (P) of the rectangle.
- The perimeter of a rectangle is given by: P = 2 * (length + width).
- Let the length be 6x and the width be 5x (since the sides are in the ratio 6:5).
Step 3: Set Up the Equation
- The equation becomes: 2 * (6x + 5x) = 131.88.
- Simplifying, we have: 2 * 11x = 131.88 → 22x = 131.88 → x ≈ 6.0.
Step 4: Calculate Length and Width
- Length = 6x = 6 * 6 = 36 cm.
- Width = 5x = 5 * 6 = 30 cm.
Step 5: Find the Area of the Rectangle
- Area (A) = Length * Width = 36 cm * 30 cm = 1080 cm².
Conclusion
The area of the rectangle formed by folding the wire is 1080 cm², which corresponds to option 'A'.
To find the area of the rectangle formed by folding a circular wire, we start with the properties of the wire and the rectangle's dimensions.
Step 1: Calculate the Circumference of the Circle
- The diameter of the circle is 42 cm.
- The circumference (C) can be calculated using the formula: C = π * diameter.
- Thus, C = π * 42 cm ≈ 131.88 cm (using π ≈ 3.14).
Step 2: Determine the Rectangle's Dimensions
- The circumference of the circle becomes the perimeter (P) of the rectangle.
- The perimeter of a rectangle is given by: P = 2 * (length + width).
- Let the length be 6x and the width be 5x (since the sides are in the ratio 6:5).
Step 3: Set Up the Equation
- The equation becomes: 2 * (6x + 5x) = 131.88.
- Simplifying, we have: 2 * 11x = 131.88 → 22x = 131.88 → x ≈ 6.0.
Step 4: Calculate Length and Width
- Length = 6x = 6 * 6 = 36 cm.
- Width = 5x = 5 * 6 = 30 cm.
Step 5: Find the Area of the Rectangle
- Area (A) = Length * Width = 36 cm * 30 cm = 1080 cm².
Conclusion
The area of the rectangle formed by folding the wire is 1080 cm², which corresponds to option 'A'.
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