Question

A chess board contains 64 equal square and the area of the each square is 6.25 square A border around the boards is 4 cm wide the length of the side of the chess board is

Answer 1

Appropriate Question :-

A chess board contains 64 equal square and the area of the each square is 6.25 square cm. A border around the boards is 4 cm wide. The length of the side of the chess board is _______

$\large\underline{\sf{Solution-}}$

Let assume that length of the side of chess board = x cm.

Let assume that ABCD be the chess board.

And

Let assume that PQRS represents the area enclosed by 64 squares.

As PQRS contains 64 equal squares of area 6.25 square cm.

So,

$\rm\implies \:Area_{(PQRS)} = 6.25 \times 64 = 400 \: {cm}^{2} - - - (1)$

The border around the PQRS is 4 cm wide

Then, Length of PQ = x - 4 - 4 = x - 8 cm

Also,

$\rm\implies \:Area_{(PQRS)} \: = \: {(x - 8)}^{2} - - - (2)$

On equating equation (1) and equation (2), we get

$\rm \: {(x - 8)}^{2} = 400$

$\rm \: x - 8 \: = \: \pm \: 20$

$\rm\implies \:\rm \: x - 8 \: = \: 20 \: \: \{side \: can \: never \: be \: - \: ve \}$

$\rm\implies \:x \: = \: 28 \: cm$

So, The length of the side of the chess board is 28 cm

$\rule{190pt}{2pt}$

Additional Information :-

Nature of roots :-

Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

If Discriminant, D > 0, then roots of the equation are real and unequal.

If Discriminant, D = 0, then roots of the equation are real and equal.

If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

Discriminant, D = b² - 4ac

Answer 2

Answer:    ∴The length of the side of the chess board is 400.04m

Step-by-step explanation:

Solution,

Here,

A chess board contains=64 square

The area of the each square = 6.25 m

The total area of 64 square = 64×6.25 m =400 m

A border around the boards = 4 cm=4÷100m=0.04 m

The length of the side of the chess board = 400+0.04m =400.04m