Question

a rectangular Park of length 64 metre and breadth is 40 meter is to be surrounded extremely by path which is 4 meter wide. find the area of the path​

Answer 1

Diagram :-

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To Find :-

The Area of the path .

Given :-

• Length of the park = 64 m

• Breadth of the park = 40 m

• Width of the path = 4 m

We know :-

Area of a Rectangle :-

$\underline{\boxed{\bf{A_{(Rectangle)} = Length \times Breadth}}}$

Concept :-

According to the Question , the Path was made around the rectangular park. , hence it makes a new Rectangle .

A/c , the difference of Area of the New Rectangle and the Area of the original one , will give the Area of the Park.

But first let us find the length and breadth of the new Rectangle.

• Length of the new Rectangle = [Length of the Original Rectangle + 2 (4)] m

==> Length of the new Rectangle = (64 + 8) m

==> Length of the new Rectangle = 72 m

Hence, the length of the New Rectangle is 72 m

• Breadth of the new Rectangle = [Breadth of the Original Rectangle + 2 (4)] m

==> Breadth of the new Rectangle = (40 + 8) m

==> Breadth of the new Rectangle = 48 m

Hence, the Breadth of the New Rectangle is 48 m

Now , by finding the individual areas of the Rectangle and by subtracting them ,we will get the required value.

Solution :-

Area of the Original Rectangle :-

Given :-

• Length = 64 m

• Breadth = 40 m

Using the formula for Area of a Rectangle and substituting the values in it , we get :-

$:\implies \bf{A = L \times B} \\ \\ \\ :\implies \bf{A = 64 \times 40} \\ \\ \\ :\implies \bf{A = 2560 m^{2}} \\ \\ \\ \therefore \purple{\bf{A = 2560 m^{2}}}$

Hence, the Area of the Rectangular Park is 2560 m².

Area of the New Rectangle :-

Given :-

• Length = 72 m

• Breadth = 48 m

Using the formula for Area of a Rectangle and substituting the values in it , we get :-

$:\implies \bf{A = L \times B} \\ \\ \\ :\implies \bf{A = 72 \times 48} \\ \\ \\ :\implies \bf{A = 3456 m^{2}} \\ \\ \\ \therefore \purple{\bf{A = 3456 m^{2}}}$

Hence, the Area of the Rectangular Park is 3456 m².

Area of the Path :-

Given :-

• Area of the original Rectangle = 2560 m²

• Area of the new Rectangle = 3456 m²

By subtracting the Area of the Original Rectangle from the Area of New Rectangle , we get :-

Area of Path = Area of New Rectangle - Area of Orginal Rectangle.

==> (3456 - 2560) m²

==> 896 m².

Hence the Area of the Path is 896 m²