Question

A square laen surrounded by the path of 2.5 m wode. Area of path is 165 square m.Find area of lawn

Answer 1

Answer:

Area of lawn = 196 m²

Step-By- Step Explanation:

Dear Friend!

Let 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

Therefore, Area of lawn = (Area of the lawn including the path) - (Area of the path)

Area of a square = (side)²

→  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

→  10x =140

•°• x = 14

→  Thus, the side of the lawn = 14 m

◀   Hence, Required the area of the lawn =   196 m². ◀

Answer 2

Side = (x+5)

ACCORDING TO THE QUESTION#



Area of a square = (side)2



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


SO, x = 140/10 = 14

Thus the side of the lawn = 14 m

The area of the lawn = 196 m²