Question

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Tu We area of the rectangle
2. Find the dimensions of the rectangular field whose length and breadth are in the ratio 6:4 and
whose area is 21600 m.
3. A wire, bent in the shape of a circle, encloses an area of 3850 cm. If the wire is now bent in the
shape of a square, find the area enclosed by the square.​

Answer 1

Answers:-

2. Given:

Ratio of length and breadth of a rectangular field = 6 : 4

Area of the field = 21600 m².

Let the length and breadth of the field be 6x , 4x m.

We know that,

Area of a rectangle = length*breadth

→ (6x) * (4x) = 21600

→ 24x² = 21600

→ x² = 21600/24

→ x² = 900

→ x² = (30)²

→ x = 30

→ length (6x) = 6*30 = 180 m

→ breadth (4x) = 4*30 = 120 m.

Therefore, the dimensions of the field are 180 m and 120 m.

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3. Given:

Area of the circle formed through a wire = 3850 cm²

We know that,

Area of a circle = πr²

→ πr² = 3850

→ 22/7 * r² = 3850

→ r² = 3850 * 7/22

→ r² = 1225

→ r² = (35)²

→ r = 35 cm

The wire is bent and made into a circular shape . That means , the length of the wire = Perimeter of the circle and it is again bent to form a square.

Hence,

Perimeter of the circle = perimeter of the square.

We know that,

Perimeter of a circle = 2πr

and,

Perimeter of a square = 4 * a [length of any side]

Hence,

→ 2πr = 4a

Putting the values we get,

→ 2 * 22/7 * 35 = 4a

→ (2) * (22/7) * (35) * (1/4) = a

→ a = 1540/28

→ a = 55 cm

We know that,

Area of a square = a²

Hence,

Area of the square formed = 55 * 55

→ Area of the square formed = 3025 cm²

Therefore, the area enclosed by the square is 3025 cm².