Question

A path uniform width 2.5m made all around outside the square path of area 8100 metre square .Find perimeter of whole park included the path​

Answer 1

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

$\:\:$

$\large{\green{\underline \bold{\tt{Given :-}}}}$

$\:\:$

• Width of path = 2.5 m

$\:\:$

• Area of square = 8100 sq. m

$\:\:$

• Paths is created all around the square park from outside

$\:\:$

$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

$\:\:$

• Perimeter of whole park included the path

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

• Let the side of square park be "x"

$\:\:$

$\underline{\bold{\texttt{Area of square :}}}$

$\:\:$

➠ Side × Side

$\:\:$

➜ x × x = x²

$\:\:$

Given that area of square is 8100 sq. m

$\:\:$

➜ x² = 8100

$\:\:$

$x = \sqrt {8100 }$

$\:\:$

• x = 90
• x = -90

$\:\:$

As length can't be negative hence

$\:\:$

➨ x = 90 m

$\:\:$

$\underline{\bold{\texttt{Side of whole park including the path :}}}$

$\:\:$

• Let th new side be "y"

$\:\:$

• Width of path = 2.5 m

$\:\:$

〚 As path is created all around the park hence we will add 2 × 2.5 to the side 〛

$\:\:$

New side = 90 + 2 × 2.5

$\:\:$

➜ y = 90 + 5

$\:\:$

➨ y = 95 m

$\:\:$

$\underline{\bold{\texttt{Perimeter of square :}}}$

$\:\:$

➠ 4 × Side

$\:\:$

$\underline{\bold{\texttt{Perimeter of whole park including the path :}}}$

$\:\:$

➠ 4 × Side

$\:\:$

➜ 4 × 95

$\:\:$

➨ 380 m

$\:\:$

• Hence perimeter of whole park including the path is 380 m

$\:\:$

Additional information

$\:\:$

Properties of square

$\:\:$

• The diagonals of a square bisect each other and meet at 90°.

• The diagonals of a square bisect its angles.

• Opposite sides of a square are both parallel and equal in length.

• All four angles of a square are equal and each one is a right angle.

• All four sides of a square are equal.

Answer 2

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

$\:\:$

$\large{\green{\underline \bold{\tt{Given :-}}}}$

$\:\:$

• Width of path = 2.5 m

$\:\:$

• Area of square = 8100 sq. m

$\:\:$

• Paths is created all around the square park from outside

$\:\:$

$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

$\:\:$

• Perimeter of whole park included the path

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

Let the side of square park be "x"

$\:\:$

$\underline{\bold{\texttt{Area of square :}}}$

$\:\:$

➠ Side × Side

$\:\:$

➜ x × x = x²

$\:\:$

Given that area of square is 8100 sq. m

$\:\:$

➜ x² = 8100

$\:\:$

$x = \sqrt {8100 }$

$\:\:$

x = 90

x = -90

$\:\:$

As length can't be negative hence

$\:\:$

➨ x = 90 m

$\:\:$

$\underline{\bold{\texttt{Side of whole park including the path :}}}$

$\:\:$

Let th new side be "y"

$\:\:$

Width of path = 2.5 m

$\:\:$

〚 As path is created all around the park hence we will add 2 × 2.5 to the side 〛

$\:\:$

New side = 90 + 2 × 2.5

$\:\:$

➜ y = 90 + 5

$\:\:$

➨ y = 95 m

$\:\:$

$\underline{\bold{\texttt{Perimeter of square :}}}$

$\:\:$

➠ 4 × Side

$\:\:$

$\underline{\bold{\texttt{Perimeter of whole park including the path :}}}$

$\:\:$

➠ 4 × Side

$\:\:$

➜ 4 × 95

$\:\:$

➨ 380 m

$\:\:$

• Hence perimeter of whole park including the path is 380 m

$\:\:$