Question

1. The total area of 64 small squares of a chessboard is 400cm. There is a 3 cm wide border around the chessboard. What is the length of each side of the chessboard?

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Answer 1

Answer:

26cm

Step-by-step explanation:

Number of squares in the chess board = 64

Total Area of 64 small squares in the chess board = 400 $cm^{2}$

So, are of 1 small square = 400/64 = 6.25 $cm^{2}$

Now, we know that area of a square = S X S = $S^{2}$ where S is the sides of the square

Therefore,  $S^{2}$ = 6.25

S = 2.5 cm

Now, there are 8 small squares on each side of the chess board

Therefore, length of each side of the board (excluding the borders) = 8 X 2.5 = 20 cm

Now there is 3cm border on each side

Therefore, length of each side of the board including the borders = 20 + 3 + 3 = 26cm

                                                         ALTERNATIVE

Number of squares in the chess board = 64

Total Area of 64 small squares in the chess board = 400 $cm^{2}$

The chess board is a square

Now, we know that area of a square = S X S = $S^{2}$ where S is the sides of the chess board (excluding the boarders)

Therefore, total length of the chess board excluding the borders = $\sqrt{400}$ = 20cm

Now there is 3cm border on each side

Therefore, length of each side of the board including the borders = 20 + 3 + 3 = 26cm

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Answer 2

Answer:

•Given

The total area of 64 small squares of a chessboard is 400cm,

There is a 3 cm wide border around the chessboard.

Step-by-step explanation:

• To find the answer first of all

We know that 64 small squares area is = 400 cm

The area of 1 small square will be = 400/64

= 6.25 cm²

We know the area of the square is = side × side

So the side of each small square = √6.25cm²

• We doing the square root of 6.25 because the area of 1 small square is 6.25 cm² to

convert into side we have to find its

square root.

= √6.25 = 2.5cm

because 2.5×2.5= 6.25cm

Since we know there are 8 squares along each side of the chess board, we have :

Side = [(8 × 2.5) + 6] cm

= 20 + 6

= 26 cm

Here 8 are the squares, 2.5 cm is the side of each

small square and After border is applied, 3cm gets added to either side of the square which will

be 6 cm.

:. Therefore the length of each side of the chessboard is 26 cm.

I hope it helps. :)