A circular lawn is surrounded by a path of uniform width 3.5 m. If the total area of the lawn plus path is 2.25 times the area of the lawn alone, find the radius of the lawn. (Use π = 3.1416 and round your answer to one decimal place)
Show answer & explanation
Correct answer: C
Explanation
Given:
Width of path = 3.5 m
Total area = 2.25 times the area of the lawn
By formula:
Area of circle = πr²
Let the radius of the lawn = r
Total radius = r + 3.5
Total area = π(r + 3.5)²
Given:
π(r + 3.5)² = 2.25πr²
(r + 3.5)² = 2.25r²
r² + 7r + 12.25 = 2.25r²
0 = 1.25r² − 7r − 12.25
5r² − 28r − 49 = 0
r = (28 + √(784 + 980)) / 10
r = (28 + √1764) / 10
r = (28 + 42) / 10
r = 7
Radius of lawn = 7.0 m