Question

A path of width 2.5 cm is constructed all along outside a rectangular park which is 70 m long and 45 m wide. Find: (i) the area of the path (ii) the area of the rectangular park​

Answer 1

Answer:

Given:-

A path of width 2.5 cm is constructed all along outside a rectangular park which is 70 m long and 45 m wide.

To find:-

Find the following :

(i) the area of the path ?

(ii) the area of the rectangular park ?

Solution:-

Method-1:-

Length of the rectangular park (l)= 70 m

Breadth of the rectangular park (b)= 45 m

Area of a rectangle = Length × Breadth sq.units

Area of the rectangle = l×b sq.units

Area of the rectangular park

= 70×45 sq.m

= 3150 sq.m

Area of the rectangular park = 3150 sq.m

Width of the path (w)= 2.5 cm

We know that 1 m = 100 cm

1 cm = 1/100 m

2.5m = 2.5/100 m = 0.025 m

If it is constructed all around outside of the park then it is increased by all sides

Length of the new rectangle = l+2w

=>70+2(0.025)

=>70+0.050

=>70.05 m

Length of the new rectangle = 70.05 m

Breadth of the new rectangle =b+2w

=>45+2(0.025)

=>45+0.050

=>45.05 m

Breadth of the new rectangle = 45.05m

We have measures of the outer rectangular park are 70.05m and 45.05m

Area of the outer rectangular park = l×b sq.units

=>70.05×45.05 sq.m

=>3155.7525 sq.m

Area of the outer rectangular park = 3155.7525 sq.m

And we have

Area of the inner rectangular park = 3150 sq.m

Area of the path =

Area of the outer rectangular park - Area of the inner rectangular park

=>3155.7525 - 3150

=>5.7525 sq.m

We know that

1 sq.m = 10000 sq.cm

5.7525 sq.m = 5.7525×10000 sq.cm

Area of the Path =57525 sq.cm

Method-2:-

Length of the rectangular park (l)= 70 m

Breadth of the rectangular park (b)= 45 m

Width of the path (w)= 2.5 cm

We know that 1 m = 100 cm

1 cm = 1/100 m

2.5m = 2.5/100 m = 0.025 m

Area of the path = 2w(l+b+2w) sq.units

=>2(0.025)(70+45+2(0.025) sq.m

=>(0.05)(70+45+0.05) sq.m

=>(0.05)(115.05) sq.m

=>5.7525 sq.m

We know that

1 sq.m = 10000 sq.cm

5.7525 sq.m = 5.7525×10000 sq.cm

Area of the Path =57525 sq.cm

Answer:-

i) Area of the Path = 5.7525 sq.m or 57525 sq.cm

ii)Area of the new rectangular park = 3155.7525 sq.m

Used formulae:-

• Area of a rectangle = Length × Breadth sq.units
• Area of the path =
• Area of the outer rectangular park - Area of the inner rectangular park
• If the 'w' is the width of the path is constructed all around outside of the rectangular park whose length and breadth are 'l' and 'b' respectively, then Area of the path = 2w(l+b+2w) sq.units
• 1 m = 100 cm
• 1 sq.m = 10000 sq.cm
• 1 cm = 1/100=0.01 m