Question

A rectangular field has a path 5m wide running around it . If the rectangle formed by the path and the field is 200m × 60m , find (i) the area of the path, and (ii) the cost of constructing the path at ₹15 per m².
Give the accurate answer stepwise. The one who gives the accurate answer stepwise will be marked as brainliest. Think properly and then give the appropriate answer stepwise. Proper Steps are must.​

Answer 1

GIVEN :

• A rectangular field has a path 5 m wide.
• Rectangle is of 200m × 60m.

TO FIND :

1. The area of the path.
2. The cost of constructing the path at ₹ 15 per m².

FORMULAS TO BE USED :

• Perimeter : 2 (length + breadth).
• Area = length × breadth.

SOLUTION :

To find the area of the path = ?

Perimeter = 2 (length + breadth).

➠ 2(200 + 60)

➠ 520 m

Area of the path = length × width.

➠ 520 × 5

➠ 2600 m²

Cost of construction = area × cost per m².

➠ 2600 × 15

➠ ₹ 39000

✦ The area of the path is 2600 m².

✦ Cost of construction is ₹ 39,000.

Answer 2

${\huge{\underline{\underline{\rm{Question:-}}}}}$

Q) A rectangular field has a path 5m wide running around it . If the rectangle formed by the path and the field is 200m × 60m , find

(i) The area of the path &

(ii) The cost of constructing the path at Rs 15 per m²

${\huge{\underline{\underline{\rm{Answer\checkmark}}}}}$

☆ Given :

• Length of rectangle = 200 m
• Breadth of rectangle = 60 m
• A 5m wide path goes around it .

☆ To Find :

1. The area of the path
2. The cost of constructing path at Rs 15 per m²

☆ Solution :

1. The area of the Path .

As you can see in the figure ,

For ABCD -

• AB = length = 200 m
• BC = breadth = 60 m

For EFGH -

• EF = length = 200 + 5 + 5 = 210 m
• FG = breadth = 60 + 5 + 5 = 70 m

Area of the path = area of EFGH - area of ABCD

$\rm \: area \: of \: the \: path = 210 \times 70 - 200 \times 60 \: {m}^{2}$

$\mapsto \rm \: area \: of \: path = 14700 - 1200 \: {m}^{2}$

$\mapsto \pink{ \boxed{ \rm \: area \: of \: the \: path = 2700 \: {m}^{2} }}$

2. Cost of Constructing path @ 15 per m²

$\mapsto \rm \: cost = rate \times area$

$\mapsto \rm \: cost = rs \: 15 \times 2700$

$\mapsto \purple{ \boxed{ \rm \: cost = rs \: 40500}}$

_________________________

# Note : If the path is inside then we would subtract 2×width of path to get the new rectangle , then we would subtract the area of the new small rectangle from the big rectangle to get the area .