Question

the vertices of a sqare lie on a circle of radius 7cm.find the ratio of the perimeters of the sqare and the circle.​

Answer 1

Answer:

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Answer 2

Answer:

..

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Step-by-step explanation:

Diameter of the circle = Diagonal of the square inscribed in it

Diagonal = 2 × 7 cm = 14 cm

Let the length of the side of the square be 'x' cm

Then using pythagorus theorem,

${x}^{2} + {x}^{2} = {(14)}^{2} \\ 2 {x}^{2} = 196 \\ {x}^{2} = 98 \\ x = 7 \sqrt{2}$

Perimeter of square

$= 4 \times 7 \sqrt{2} \\ = 28 \sqrt{2}$

Cicumference of the circle

$= 2\pi \: r \\ = 2 \times \frac{22}{7} \times 7 \\ = 44$

Ratio

$\frac{28 \sqrt{2} }{44} \\ = \frac{7 \sqrt{2} }{11}$