Question

A circle of radius 7 cm is to be cut do that it becomes the largest possible square

Answer 1

To have the largest possible square inside the circle:

⇒ the diameter of the circle is the diagonal of the circle

------------------------------------------------------------------------------------------------

Find the diameter:

Diameter = Radius x 2

Diameter = 7 x 2 = 14 cm

------------------------------------------------------------------------------------------------

Find the length of the square:

Let the length be x

a² + b² = c²

x² + x² = 14²

2x² = 196

x² = 196 ÷ 2

x² = 98

x = √98

x = 7√√2

------------------------------------------------------------------------------------------------

Area of the square:

Area = Length x Length

Area = 7√2 x 7√2 = 98 cm²

------------------------------------------------------------------------------------------------

Answer: The length of the square is 7√2 and the area is 98 cm²

------------------------------------------------------------------------------------------------