Question

The four corners of a square chessboard touch the edge of a round table. The length of the chessboard is 1 foot. Find the length of the radius of the table

Answer 1

Answer:

$\frac{\sqrt{2} }{2}\,\,foot$

Step-by-step explanation:

Given: Four corners of a square chessboard touch the edge of a round table. The length of the chessboard is 1 foot.

To find: length of the radius of the table

Solution:

Diameter of the round table is equal to the diagonal of a square chessboard.

Diagonal of a square chessboard = $\sqrt{2}$ × side of the square chessboard

Here, side of a square chessboard = 1 foot

So,

Diagonal of a square chessboard = $\sqrt{2}$ × 1 = $\sqrt{2}$ foot

Diameter of the round table = Diagonal of a square chessboard = $\sqrt{2}$ foot

Radius of the round table = Diameter of the round table/2

= $\frac{\sqrt{2} }{2}\,\,foot$