Previous Year Questions

Let length and breadth of given rectangle are in the ratio a: 3 respectively.

Perimeter of rectangle = 112 cm = 2 x (length + breadth)

Length = 56 - breadth

Side of square = (2/3) x breadth of rectangle

Area of square = area of circle (let radius of circle = r cm)

From A:

Ratio of length to breadth = 4: 3

Length = (4/3) x breadth

56 - breadth = (4/3) x breadth

Breadth = 24 cm

Side of square = 24 x 2/3 = 16 cm

Area of circle = (22/7) x r² = area of square = 16 x 16

r = 9 cm (approx.) > 8 cm

Hence, these values are possible.

From B:

Ratio of length to breadth = 6: 3 = 2: 1

Length = 2 x breadth

56 - breadth = 2 x breadth

Breadth = 56/3 cm

Side of square = (56/3) x 2/3 = 112/9 cm

Area of circle = (22/7) x r² = area of square = (112/9) x (112/9)

r = 7 cm (approx.) > 6.5 cm

Hence, these values are possible.

From C:

Ratio of length to breadth = 7: 3

Length = (7/3) x breadth

56 - breadth = (7/3) x breadth

Breadth = 84/5 cm

Side of square = (84/5) x 2/3 = 56/5 cm

Area of circle = (22/7) x r² = area of square = (56/5) x (56/5)

r = 6.31 cm (approx.) > 5.8 cm

Hence, these values are possible.

From D:

Ratio of length to breadth = 8: 3

Length = (8/3) x breadth

56 - breadth = (8/3) x breadth

Breadth = 168/11 cm

Side of square = (168/11) x 2/3 = 112/11 cm

Area of circle = (22/7) x r² = area of square = (112/11) x (112/11)

r = 5.74 cm (approx.) < 8.4 cm

Hence, these values are not possible.