Question

A rectangular park is 90m long and 70m broad. A path 6m wide is to be built around the inside of the park. Find the arra of the path. Also find the area of the remaining park in hectares.

Answer 1

Step-by-step explanation:

Given :-

A rectangular park is 90m long and 70m broad. A path 6m wide is to be built around the inside of the park.

To find:-

Find the arra of the path. Also find the area of the remaining park in hectares.

Solution:-

Length of the rectangular park= 90 m

Breadth of the rectangular park = 70 m

Area of a rectangle = lb sq.units

Area of the given rectangular park

=> 90×70 sq.m

=> 6300 sq.m

Area of the given rectangular park = 6300 sq.m

and given that

Width of the path = 6 m

If the path built around the inside of the park then the smaller rectangle will be formed

Length of the inner rectangle = l-2w units

=> 90- 2(6)

=> 90-12

=> 78 m

Breadth of the inner rectangle= b-2w units

=> 70-2(6)

=> 70-12

=> 58 m

Area of the inner rectangle

=>78×58 sq.m

=> 4524 sq.m

Area of the path = Area of the outer rectangle - Area of the inner rectangle

=> 6300-4524

=> 1776 sq.m

Area of the path = 1776 sq.m

Total area of the rectangular park = 6300 sq.m

Area of the path = 1776 sq.m

Area of the remaining park = 6300-1776

=>4524 sq.m

We know that

1 hectare = 10000 sq.m

=> 1 sq.m = 1/10000 hectares

=> 4524 sq.m = 4524/10000 hectares

=> 0.4524 hectares

Answer:-

Area of the path = 1776 sq.m

Area of the remaining park = 0.4524 hectares

Used formulae:-

• Area of a rectangle = lb sq.units

• 1 Hectare = 10000 sq.m

Answer 2

Answer:

• Area of the path = 1776 m² = 0.1776 hectare

• Area of the remaining park = 4524 m² = 0.4524 hectare

Step-by-step explanation:

Given:

Length of the park = 90 m

Breadth of the park = 70 m

A path is built inside the park.

Width of the park = 6 m

To find:

• The area of the path.
• The area of the remaining park in hectares.

Solution:

Length of the park, AB = 90 m

Breadth of the park, BC = 70 m

Length of the remaining park, PQ = (90 - 2×6 ) = 90 - 12 = 78 m

Breadth of the remaining park, QR  = 70 m = (70 - 2×6 ) = 70 - 12 = 58 m

Ar. of the path = Ar. rect. ABCD - Ar. rect. PQRS

                        = {(90×70) - (78×58)} m²

                        = {6300 - 4524} m²

                        = 1776 m²

Hence,

Area of the path = 1776 m² = 0.1776 hectare

Area of the remaining park = Ar. rect. PQRS

                                             = (78×58) m²

                                             = 4524 m²

Hence,

Area of the remaining park = 4524 m² = 0.4524 hectare

Know more:

10000 m² = 1 hectare

Area of rectangle = l×b