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.
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Answers
Answer:
square lawn surrounded by path -2.5 m wide
area of path - 165 m²
side of lawn -x
side of lawn including path - x + 2 (2.5 ) = x + 5
area of square - side * side
x² = ( x+5)- 165
x² = (x²+10x+25)
x²= x² + 10x-140
x² = 140 - x² =10x
-140 = -10x
140= 10x
x =140/10 =14
side of lawn is 14m
14 *14 is 196 m²
Step-by-step explanation:
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