Question

the path 3.5 M wide runs inside along the boundary of a square field whose side is 65 m. find the area of the path. also find the cost of construction of path if rate is Rs 25 per square metre.​

Answer 1

Solution :-

Given : The path 3.5 m wide runs inside along the boundary of a square field whose side is 65 m.

Area of square field = (side × side) sq. units

= (65 × 65) m²

= 4225 m²

Side of square field without the path = 65 - (2 × 3.5) m

= 65 - 7 = 58 m

Area of square field without path = (58 × 58) m²

= 3364 m²

Now,

Area of path = Area of square field - Area of square field without path

= (4225 - 3364) m²

= 861 m²

Cost of construction of path at Rs 25 per square metre :

1 m² = Rs 25

861 m² = Rs (861 × 25) = Rs 21525

Hence,

Area of path = 861 m²

Cost of construction of path = Rs 21525

Answer 2

Solution :-


Here,

It is given that

Width of the path that runs inside along the boundary of a square field = 3.5 m

Side of the Square field = 65 m

Now, Area of the square field along with the path
$= {a}^{2} \\ = {65}^{2} \\ = 4225 \: {m}^{2}$

Again, Area of the square field except the path
$= 65 - (2 \times 3.5) \\ = 58 \: m$

So, Area of the square field except the path
$= {a}^{2} \\ = {58}^{2} \\ = 3364 \: {m}^{2}$


Therefore, Area of the path
$= (4225 - 3364) \: {m}^{2} \\ \\ = 861 \: {m}^{2}$


Hence, the cost of constructing the path at Rs. 25 per square metre

$= 861 \times 25 \\ =rs. 21525$

Thanks!!