Question

A chess board contains 64 equal squares and the area of each square is \[\text{6}\text{.25c}{{\text{m}}^{\text{2}}}\]. A border round the board is 2cm wide. Find the length of the side of the chess board.

Answer 1

Hint: Given a chessboard with 64 equal squares, and the area of each square is \[\text{6}\text{.25c}{{\text{m}}^{\text{2}}}\]. Find the length of the side of each small square. Note that, a chessboard contains 64 equal squares arranged in an 8×8 grid. Therefore find the length of one side of the chessboard. Given that a border around the board is 2cm wide. Hence, find the length of the side of the chessboard taking twice the length of the border in the count.

Complete step-by-step solution:

We know that a chess board contains 64 equal squares arranged in an 8×8 grid.

Remember that if we have square of side a cm then, area of square will be \[\text{a c}{{\text{m}}^{\text{2}}}\]
Given that, the area of each square is \[\text{6}\text{.25c}{{\text{m}}^{\text{2}}}\].
So, to evaluate the length of the side of each square, we will take the square root on both sides.
Taking square root on both sides, we get
The side-length of each square is $\sqrt{6.25}=2.5$ cm
As a chess board contains 64 equal squares arranged in an 8×8 grid,
So, the length of a side of the chessboard is 8×2.5 = 20 cm
Now, given that there is a border around the board of 2cm width.
So, the length of the side of the chessboard (with border) is $20+2+2=24$ cm.

Note: Note that, a chess board contains 64 equal squares arranged in an 8×8 grid. Also, remember that if we have a square of side a cm then, the area of the square will be \[\text{a c}{{\text{m}}^{\text{2}}}\]. Always mention units after the final numerical answer. Try to avoid calculation mistakes.