Question

1. kai is making a chessboard using pieces of wood that measure 1 square inch. when he finishes, the chessboard will have an area of 64 square inches. how many pieces of wood should he put along each side?

a 64 pieces of wood
b 64² pieces of wood
c 8 pieces of wood
d 8² pieces of wood

Explanation:

Step1: Recall the area of a square formula

The area \( A \) of a square is given by \( A = s^2 \), where \( s \) is the length of a side. Here, the chessboard is a square (since a chessboard has equal sides), and the area of the chessboard is 64 square inches. Each piece of wood is 1 square inch, so the number of pieces along each side relates to the side length of the square chessboard.

Step2: Solve for the side length \( s \)

We know \( A = s^2 = 64 \). To find \( s \), we take the square root of both sides: \( s=\sqrt{64} \). Calculating the square root, \( \sqrt{64} = 8 \). This means the side length of the chessboard (in terms of the number of 1 - square - inch pieces) is 8. So, Kai should put 8 pieces of wood along each side.

Answer:

C. 8 pieces of wood