Question

A square lawn is surrounded by a path 2.5 M wide if the area of the path is 165 CM square find the area of the lawn​

Answer 1

Answer:

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(2.5m) = x + 5m  

So, area of lawn = (Area of the lawn including the path) - (Area of the path)  

Area of a square = (side)2  

Therefore, we say :  

x2 = (x + 5)2 – 165 m2

x2 = (x2 + 10x +25) - 165m2

x2 = x2+ 10x + 25 - 165  

x2 = x2 + 10x - 140  

x2 - 140 = x2 - 10x  

x2 - x2 - 140 = -10x  

-140 = -10x  

i.e 140 = 10x  

Therefore x = 140/10 = 14  

Since the side of the lawn = 14 m  

The area of the lawn = (14)2 or 196 m2.