Question

The circumference of a circular field and the perimeter of a square field are equal. If the area of the square field is 484m2, then the length of the diameter of the circular field is _______m.

Answer 1

Step-by-step explanation:

here is your answer....

Answer 2

Given:-

• Circumference of a circular field is equal to the perimeter of a square.
• Area of the square = 484 m²

To find:-

The length of diameter of the circular field.

Solution:-

Area of square = 484 m²

We know,

Area of square = (side)²

= $\sf{484 = (side)^2}$

=> $\sf{side = \sqrt{484}}$

=> $\sf{side = 22}$

Now,

Perimeter of the square = 4×side

$\sf{Perimeter = 4\times 22}$

= $\sf{Perimeter = 88\:m}$

ATQ,

Perimeter of square = Circumference of the circle.

$\sf{88 = 2\pi r}$

= $\sf{88 = 2\times \dfrac{22}{7}\times r}$

= $\sf{\dfrac{88\times7}{22\times2} = r}$

= $\sf{2\times7 = r}$

= $\sf{14 = r}$

=> $\sf{r = 14\:m}$

We know,

Diameter of a circle = 2×radius

= $\sf{Diameter = 2\times14}$

= $\sf{Diameter = 28\:m}$

Therefore length of diameter of the circular field is 28 m

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Formula used:-

• Area of square = (side)² sq.units
• Perimeter of square = 4×side units
• Circumference of circle = 2πr units
• Diameter of circle = 2×radius

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