Question

A square lawn is surrounded by a path 2.5 m wide. If the area of the path is 165 m2, find
the area of the lawn.
​

Answer 1

$\sf\small\underline\purple{Let:-}$

$\tt{\implies Side\:_{(square)}=x}$

$\sf\small\underline\purple{Given:-}$

$\tt{\implies Area\:_{(path)}=165m^2}$

$\tt{\implies Wide\:_{(path)}=2.5m}$

$\sf\small\underline\purple{To\: Find:-}$

$\tt{\implies Area\:_{(square\:lawn)}=?}$

$\sf\small\underline\purple{Solution:-}$

To calculate the area of lawn , at first we have to assume the side of lawn be x. After that we have to add the side of lawn with the wide of path as given in the question that lawn is surrounded by a path of 2.5. wide. As per the question we have to set up equation then simply simplify the expression. By solving we get the value of x then calculating the area of lawn.

$\tt{\implies Side\:_{(for\:lawn\: with\:path)}=x+2(2.5)}$

$\tt{\implies Side\:_{(for\:lawn\: with\:path)}=x+5}$

$\sf\small\underline\purple{As\:per\:the\: above\: condition:-}$

$\tt{\implies Area\:_{(lawn)}=Area\:_{(for\:lawn\: with\:path)}-Area\:_{(path)}}$

$\tt{\implies (x)^2=(x+5)^2-165}$

$\tt{\implies x^2=x^2+10x+25-165}$

$\tt{\implies x^2-x^2-10x=25-165}$

$\tt{\implies -10x=-140}$

$\tt{\implies 10x=140}$

$\tt{\implies x=14m}$

$\sf\large{Hence,}$

$\tt{\implies Area\:_{(square\:lawn)}=side^2}$

$\tt{\implies Area\:_{(square\:lawn)}=x^2}$

$\tt{\implies Area\:_{(square\:lawn)}=14^2}$

$\tt{\implies Area\:_{(square\:lawn)}=196m^2}$

Answer 2

${\large{\bold{\rm{\underline{Question}}}}}\; \; \; \; \red \bigstar$

✪ A square lawn is surrounded by a path 2.5 m wide. If the area of the path is 165 m² find the area of the lawn.

${\large{\bold{\rm{\underline{Given \; that}}}}}\; \; \; \; \red \bigstar$

✠ Square lawn is surrounded by a path and it's 2.5 metres in breadth.

✠ The area of the path is 165 m²

${\large{\bold{\rm{\underline{To \; find}}}}}\; \; \; \; \red \bigstar$

✠ Area of the lawn.

${\large{\bold{\rm{\underline{Solution}}}}}\; \; \; \; \red \bigstar$

✠ Area of the lawn = 196 m²

${\large{\bold{\rm{\underline{Assumption}}}}}\; \; \; \; \red \bigstar$

✠ Let a be the side of the square lawn.

${\large{\bold{\rm{\underline{Using \; concept}}}}}\; \; \; \; \red \bigstar$

✠ Formula to find area of square.

✠ Formula to find area of the lawn (According to the question)

${\large{\bold{\rm{\underline{Using \; formula}}}}}\; \; \; \; \red \bigstar$

✠ Area of square = Side × Side or (Side)²

✠ Area of lawn (side) = Area of lawn surrounded by path - Area of path.

${\large{\bold{\rm{\underline{Full \; Solution}}}}}\; \; \; \; \red \bigstar$

_________________

~ As in the question it is already said that there is a square lawn and it is surrounded by a path that is 2.5 m as it's breadth. And it's also given that the area of the path is 165 m² and at last we have to find the area of the lawn.

~ As we already assume a as the side of the square lawn.

~ Let's solve this question properly by using all the above information..!

_________________

~ Firstly let us find the area of the lawn with the path.

➙ Area of lawn with the path = a+2(2.5)

➙ Area of lawn with the path = a + 2 × 2.5

➙ Area of lawn with the path = a + 5

_________________

~ Now according to the question,

Area of lawn (side) = Area of lawn surrounded by path - Area of path.

➙ a² = (a+5)² - 165

➙ a² = a² + 10a + 25 - 165

➙ a² - a² - 10a = 25 - 165

➙ -10a = -140

➙ 10a = 140

➙ 1a = 14

➙ a = 14

_________________

~ Now according to the question, let us use formula to find area of square and let us find area of lawn now.

➙ Area = Side × Side

➙ Area = 14 × 14

➙ Area = 196 m²

_________________

${\large{\bold{\rm{\underline{Extra \; knowledge}}}}}\; \; \; \; \red \bigstar$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Area \: of \: rectangle \: = \: Length \times Breadth}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Perimeter \: of \: rectangle \: = \:2(length+breadth)}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Perimeter \: of \: square \: = \: 4 \times sides}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Area \: of \: square \: = \: Side \times Side}}}$