Question

the diameters of two circles in the ratio 3 ratio 4 and the sum of the areas of the circle is equal to the area of circle whose diameter measured 30 cm find the diameter of the given circles​

Answer 1

Answer:

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

Step-by-step explanation:

Let the ratio be x

diameter of first circle = 3x , radius of first circle = 3x/2

diameter of second circle = 4x , radius of second circle = 2x

now it is given ,

Area of 1st circle + Area of 2nd circle = area of circle with radius 15cm

pi (3x/2)^2 + pi (2x)^2 = pi (15)^2

9x^2/4 + 4x^2 = 225

25x^2 = 900

x = 6

Diameter of first circle = 3 × 6 = 18 cm

diameter of second circle = 4 × 6 = 24 cm