A square is surrounded by a path 2.5 m wide. If the area of the path is 165 m2, find the area of lawn
Answers
Answer:
\sf\small\underline\purple{Let:-}
Let:−
\tt{\implies Side\:_{(square)}=x}⟹Side
(square)
=x
\sf\small\underline\purple{Given:-}
Given:−
\tt{\implies Area\:_{(path)}=165m^2}⟹Area
(path)
=165m
2
\tt{\implies Wide\:_{(path)}=2.5m}⟹Wide
(path)
=2.5m
\sf\small\underline\purple{To\: Find:-}
ToFind:−
\tt{\implies Area\:_{(square\:lawn)}=?}⟹Area
(squarelawn)
=?
\sf\small\underline\purple{Solution:-}
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)}⟹Side
(forlawnwithpath)
=x+2(2.5)
\tt{\implies Side\:_{(for\:lawn\: with\:path)}=x+5}⟹Side
(forlawnwithpath)
=x+5
\sf\small\underline\purple{As\:per\:the\: above\: condition:-}
Aspertheabovecondition:−
\tt{\implies Area\:_{(lawn)}=Area\:_{(for\:lawn\: with\:path)}-Area\:_{(path)}}⟹Area
(lawn)
=Area
(forlawnwithpath)
−Area
(path)
\tt{\implies (x)^2=(x+5)^2-165}⟹(x)
2
=(x+5)
2
−165
\tt{\implies x^2=x^2+10x+25-165}⟹x
2
=x
2
+10x+25−165
\tt{\implies x^2-x^2-10x=25-165}⟹x
2
−x
2
−10x=25−165
\tt{\implies -10x=-140}⟹−10x=−140
\tt{\implies 10x=140}⟹10x=140
\tt{\implies x=14m}⟹x=14m
\sf\large{Hence,}Hence,
\tt{\implies Area\:_{(square\:lawn)}=side^2}⟹Area
(squarelawn)
=side
2
\tt{\implies Area\:_{(square\:lawn)}=x^2}⟹Area
(squarelawn)
=x
2
\tt{\implies Area\:_{(square\:lawn)}=14^2}⟹Area
(squarelawn)
=14
2
\tt{\implies Area\:_{(square\:lawn)}=196m^2}⟹Area
(squarelawn)
=196m
2
Answer:
Consider the side of the lawn be x
Given width of the path 2.5m
Side of the lawn including path x+2(2.5)=x+5
Area of a square =(side)
2
So, area of lawn = (Area of the lawn including the path) - (Area of the path)
Therefore, According to the given question,:
x
2
=(x + 5)
2
−165
x
2
=(x
2
+ 10x +25)−165m
2
x
2
=x
2
+10x+25−165
x
2
=x
2
+10x−140
x
2
−140=x
2
−10x
x
2
−x
2
−140=−10x
−140=−10x
i.e 140=10x
∴x=140/10=14
Since the side of the lawn = 14m
The area of the lawn=(14)
2
or196 m
2
.
hope it helps you