Quant Question Of The Day: 247
Find the ratio of Area of Circumcircle to the are of triangle having side 3, 4, 5. (circumcircle of the same triangle)
- 275/84
- 3/1
- 121/60
- 225/125
Find the ratio of Area of Circumcircle to the are of triangle having side 3, 4, 5. (circumcircle of the same triangle)
Answer: (1) 275/84 Solution Area of triangle by hero’s formula = [s(s-a)(s-b)(s-c)]^0.5 s= semiperimeter = (3+4+5)/2 = 6 so area = [6(3)(2)(1)]^0.5 = 6 units now area = abc /4R = 6 units , where R is circumradius 3*4*5/4R = 6 ; R = 5/2 units so area of circumcircle = 22/7 (25/4) = 275/14 units So ratio of Area = (275/14)/6 = 275/84
option 1) 275/84
The right angled triangle with sides 3K 4K 5K has inradius of K and circumradius of 2.5K.
Remember it and get the answer.