Question

a rectangular frizzy plot is 75 m long and 60 m board. it has path of width 2 m all around it on the inside. find the area of the path and cost and of constructing it at Rs 125 per m square​

Answer 1

${\large{\sf{\pmb{\underline{Understanding \; the \; question...}}}}}$

★ This question says that a rectangular frizzy plot is in the length of 75 m and it's breadth is 60 m. And now the question says that it has a path of breadth 2 m all around it on the inside. We have to find the area of the path and cost of constructing it at Rs 125 per m². Let's solve this question!

${\large{\sf{\pmb{\underline{Given \; that...}}}}}$

★ Length of a rectangular frizzy plot = 75 metres.

★ Breadth of a rectangular frizzy plot = 60 metres.

★ It has a path of breadth 2 m all around it on the inside.

${\large{\sf{\pmb{\underline{To \; find...}}}}}$

★ The area of the path

★ Cost of constructing it(path that is surrounded in a rectangular frizzy) at Rs 125 per metres²

${\large{\sf{\pmb{\underline{Solution...}}}}}$

★ The area of the path = 274 m²

★ Cost of constructing it(path that is surrounded in a rectangular frizzy) at Rs 125 per metres² = Rupees 34250

${\large{\sf{\pmb{\underline{Using \; concepts...}}}}}$

★ Formula to find area of rectangle.

★ Formula to find the cost of constructing it at Rs 125 per metres².

★ Formula to find area of the path.

${\large{\sf{\pmb{\underline{Using \; formulas...}}}}}$

★ Area of rectangle = Length × Breadth

★ Formula to find the cost of constructing it at Rs 125 per metres² = Given Rate × Area of the path.

★ Area of the path = Area of plot including path - Area of the plot

${\large{\sf{\pmb{\underline{Full \; Solution...}}}}}$

~ Firstly by using the formula to find area of rectangle, let us find the area of the plot now!

⟶ Area of rectangle = Length × Breadth

⟶ Area of plot = Length × Breadth

⟶ Area of plot = (75×60) metres

⟶ Area of plot = 4500 metres²

• Henceforth, 4500 metres² is the area of the plot.

~ Now as it is given that it has a path of breadth 2 m all around it on the inside. Means,

⟶ Length of plot including the path = 75+2 = 77 metres

⟶ Breadth of plot including the path = 60+2 = 62 metres

~ Now we have to find the area of the plot including the path by using formula to find area of rectangle!

⟶ Length of plot including the path = 77 metres

⟶ Breadth of plot including the path = 62 metres

⟶ Area of plot including the path = Length × Breadth

⟶ Area of plot including the path = (77×62) metres

⟶ Area of plot including the path = 4774 metres²

• Henceforth, the area of plot including the path is 4774 metres²

~ Now let's find the area of path by using formula!

⟶ Area of the path = Area of plot including path - Area of the plot

⟶ Area of the path = (4774-4500) m²

⟶ Area of the path = 274 m²

• Henceforth, area of the path is 274 metres².

⟶ The cost of constructing it at Rs 125 per metres² = 125 × 274

⟶ The cost of constructing it at Rs 125 per metres² = 34250 Rupees

• Henceforth, Rupees 34250 is the cost of constructing it at Rs 125 per metres².