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Answers
Answer:
Step-by-step explanation:
66 cm
Step-by-step explanation:
Define x:
Let the breadth be x
The length = 2x
Find the area of the rectangle:
Area = Length x Breadth
Area = 2x²
Find the perimeter of the rectangle:
Perimeter = 2(Length + breadth)
Perimeter = 2(2x + x)
Perimeter = 6x
Find the radius of the circle in term of x
Circumference = 2πr
2πr = 6x
r = 6x ÷ 2π
r = 3x/π
Find the area of the circle in term of x:
Area = πr²
Area = π(3x/π)² = 9x²/π
Solve x:
The area of the circle is greater than the rectangle by 104.5 cm²
9x²/π - 2x² = 104.5
x² (9/π - 2) = 104.5
19/22 x² = 104.5
x² = 104.5 ÷ 19/22
x² = 121
x = √121
x = 11 cm
Find the length of the wire:
Length = 6x = 6(11) = 66 cm
Answer: The length is 66 cm
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Answer:
66 cm
Step-by-step explanation:
Define x:
Let the breadth be x
The length = 2x
Find the area of the rectangle:
Area = Length x Breadth
Area = 2x²
Find the perimeter of the rectangle:
Perimeter = 2(Length + breadth)
Perimeter = 2(2x + x)
Perimeter = 6x
Find the radius of the circle in term of x
Circumference = 2πr
2πr = 6x
r = 6x ÷ 2π
r = 3x/π
Find the area of the circle in term of x:
Area = πr²
Area = π(3x/π)² = 9x²/π
Solve x:
The area of the circle is greater than the rectangle by 104.5 cm²
9x²/π - 2x² = 104.5
x² (9/π - 2) = 104.5
19/22 x² = 104.5
x² = 104.5 ÷ 19/22
x² = 121
x = √121
x = 11 cm
Find the length of the wire:
Length = 6x = 6(11) = 66 cm
Answer: The length is 66 cm
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