The Circumference of A Circle Is 100 Cm. The Side of a Square Inscribed In The Circle - Mathematics

The circumference of a circle is 100 cm. The side of a square inscribed in the circle is

(a) 50√2 cm

(b) 100/π cm

(c) 50√2/π cm

(d) 100√2/π cm 

(c) 50√2/π cm 

Explanation:


Given,

circumference of circle is 100 cm

There for,

2𝝅r = 100 cm.

𝝅r = `"100"/"2"`

𝝅r = 50

r = `"50"/"𝝅"`


Calculation for Diagonal

= 2 `\times` `"50"/"𝝅"`

= `"100"/"𝝅"`

∴ Diagonal = `"100"/"𝝅"`


Now,

Let side of Square = x

According formula,

= `Diagonal^{2}` = `Side^{2}` + `Side^{2}`

= `("100"/"𝝅")^{2}` = `x^{2}` + `x^{2}`

= `("100"/"𝝅")^{2}` = `2x^{2}`

= `x^{2}` = `1/2` `("100"/"𝝅")^{2}`= `\frac{1}{\sqrt{2}}\times\frac{100}{\pi}`

= `x^{2}` = `1/2` `("100"/"𝝅")^{2}`

= `\frac{1}{\sqrt{2}}\times\frac{2 \times 50}{\pi}`

=`\frac{50\sqrt{2}}{\pi}`

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