The area of a triangular field with sides 220 m, 231 m and 319 m is equal to 15 times the area of a circular garden. What is the diameter (in m) of a circular garden?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 14√11.
Given:
The area of a triangular field with sides 220 m, 231 m and 319 m = 15 times the area of a circular garden
Formula used:
Area of a right angled triangle = (1/2) × base × height
Area of circle = πr2
Where, r = radius
Calculations:
The sides of the triangle follow the Pythagoras theorem such that we have
Base = 220 m, Height = 231 and Hypotenuse = 319 m
(Hypotenuse)2 = (Base)2 + (Perpendicular)2
(319)2 = (220)2 + (231)2
According to the question,
⇒ Area of triangle = 15 × πr2
⇒ (1/2) × 220 × 231 = 15 × (22/7) × r2
⇒ r2 = 7 × 7 × 11
⇒ r = 7√11
We know that Diameter = 2 × radius
⇒ Diameter = 2 × 7√11 = 14√11