Question

A chessboard has an area of 324 square inches. There is an 1-inch border around the 64 squares on the board. What is the length of one side of the region containing the small squares?

Answer 1

Answer:

Length of one side of the region containing small squares is 16 inches.

Step-by-step explanation:

Given:

Area of the chess board = 324 square inches

Border around 64 -squares on board = 1 inch

We need to find the length containing small squares.

Solution:

Let the length of one side of the chess board be 'L'.

Now we know that;

Border around 64 -squares on board = 1 inch

So we can say that;

Length of the side of the chess board = $L+1+1 = L+2$

Now we know that;

Area of square is equal to square of its side.

framing in equation form we get;

$(L+2)^2=324$

Now taking square root on both side we get;

$\sqrt{(L+2)^2} =\sqrt{324}\\ \\L+2 = 18$

Now subtracting both side by 2 we get;

$L+2-2=18-2\\\\L=16\ in$

Hence Length of one side of the region containing small squares is 16 inches.