Question

A five rupee coin and a ten rupee coin are placed such that they touch each other.Sum of their area 117 mm^2 and distance between their centres is 15mm

Answer 1

Answer:

Radius of coins are 6 & 9 mm

Step-by-step explanation:

Let sat Radius of Rs 5 coin =  R mm

ad distance between center points = 15 mm

=> Radius of Rs 10 coin = 15 - R  mm

Area of Rs 5 coins = π R²

Area of Rs 10 coin = π (15-R)²

Total Area = π R² + π (15-R)²

π R² + π (15-R)²  = 117

=> (22/7) ( R² + 225 + R² - 30R) = 117

=> 22(2R² -30R + 225) = 819

=> 44R² - 660R + 4950 = 819

=> 44R² - 660R + 4131 = 0

Data is wrong as it gets D -ve

hence imaginary number

Let say area = π117 mm²

2R² -30R + 225 = 117

=> 2R² -30R + 108 = 0

=> R² - 15R + 54 = 0

=> R² - 9R - 6R + 54 = 0

=> R(R-9) -6(R-9) = 0

=> (R-9)(R-6) = 0

=> R = 9 or 6

Then 15 - R = 6 or 9

Radius of coins are 6 & 9 mm