OPQRS is a square and is inscribed in a circle If area of the square is 49 sq. units, find the ratio of the
perimeter of the square to the circumference of the circle.
Answers
Answer:
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Step-by-step explanation:
Correct option is B)
Area of square with side a is a2 and area of circle with radius r is πr2.
Area of square = 36 sq units.
Hence, side = 36=6 units.
As circle is inscribed in square, so the diameter of the circle = 6.
If the diameter of the circle is 6 then the radius of the circle is 3 as the radius is half of diameter.
Hence, the area of the circle is π(3)2=9π.
The ratio of the perimeter of the square to the circumference of the circle is 7:22.
Given - Area of square
Find - Ratio of the perimeter of the square to the circumference of the circle.
Solution - Diagonal of square = diameter of circle
Area of square = side²
Side = ✓area
Side = ✓49
Side = 7 units
As per Pythagoras theorem,
Diagonal of square = ✓(sum of sides)²
Diagonal = ✓(7²+7²)
Diagonal = ✓(49+49)
Diagonal = ✓98
Diagonal = 7✓2 units
Perimeter of square = 4*side
Perimeter = 4*7
Perimeter = 28 units
Circumference of circle = πd
Circumference = 22/7*28
Circumference = 22*4
Circumference = 88 units
Ratio = 28:88
Ratio = 7:22
The ratio is 7:22.
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