Question

The daimeter of two circle are a 3:4 and the sum of areas of the circles is equal to the area of a circle whose daimeter measures 30cm find the daimeter of the given circle.​

Answer 1

Given, the diameter of two circles are 3 : 4

Let the diameter of the first circle = 3x

So, radius of the first circle = 3x/2

and diameter of the second circle = 4x

So, radius of the second circle = 4x/2 = 2x

Now, according to question,

π(3x/2)2 + π(2x)2 = π(30/2)2

=> (3x/2)2 + (2x)2 = (15)2

=> 9x2 /4 + 4x2 = 225

=> (9x2 + 16x2 )/4 = 225

=> 25x2 /4 = 225

=> x2 /4 = 225/25

=> x2 /4 = 9

=> x2 = 9*4

=> x2 = 36

=> x = √36

=> x = ±6

=> x = 6 {since x ≠ -6}

So, the the diameter of the first circle = 3x = 3*6 = 18 cm

and the diameter of the second circle = 4x = 4*6 = 24 cm

Answer 2

Answer:

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