Question

the perimeter of a circle is 220 cm. The area of a square inscribed in it is....

Solve it with full explanation.

No searching from google

Answer 1

→Perimeter=Circumference of circle
→Circumference=220cm
→C=2πr
→220=2×22/7×r
→220×7/44=r
→35=r

→d=2r
→d=2×35
→d=70cm
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Diameter of circle=Diagonal of square

Let side of square be x
Using Pythagoras theorem
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→x²+x²=70²
→2x²=4900
→x²=2450
→x=√2450
→x=49.49cm²

Area=S×S

Area=2449.20=2450cm²

Answer 2

It is given that the perimeter ( or circumference ) of the circle is 220 cm.


From the properties of circle, We know : -

• Circumference of circle = 2πr, where r is the radius of the circle.


Now, comparing the circumference of the circle with the formula given above,

= > 2πr = 220 cm

$= > 2 \times \dfrac{22}{7} \times r = 220 \: cm \\ \\ \\ = > r = 220 \times \dfrac{7}{22} \times \frac{1}{2} \: cm \\ \\ \\ = > r = 35 \: cm$




On onbserving ( the diagram ), we get :
Diameter is same is the diagonal of the square.

Therefore,
Diagonal of square = Diameter of circle

Diagonal of square = 2 x radius = 2 x 35 cm = 70 cm


Now,
Let the side of the square be a cm,

By Pythagoras Theorem :

= > ( side )² + ( side )² = ( diagonal )²

= > a² + a² = ( 70 cm )²

= > 2a² = 4900 cm²

= > a² = 2450 cm²




Now,
a² = 2450 cm² = ( side )² = Area of square.

Therefore,
Area of the square is 2450 cm^2
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