The radii of two circles are 8 cm and 15 cm. Find the perimeter of the circle having area equal to the sum of the areas of the two circles (in cm).

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Step 1: Calculate the area of the first circle with radius r1 = 8 cm.
Area1 = π * r1^2 = π * 8^2 = 64π cm².

Step 2: Calculate the area of the second circle with radius r2 = 15 cm.
Area2 = π * r2^2 = π * 15^2 = 225π cm².

Step 3: Sum of the areas = Area1 + Area2 = 64π + 225π = 289π cm².

Step 4: Let the radius of the new circle be R. Its area is equal to the sum of the two areas.
So, π * R^2 = 289π
=> R^2 = 289
=> R = √289 = 17 cm.

Step 5: The perimeter (circumference) of the new circle is 2 * π * R = 2 * π * 17 = 34π cm.

Step 6: Using π ≈ 3.1416, perimeter ≈ 34 * 3.1416 = 106.8144 cm.

Therefore, the perimeter of the circle is approximately 107 cm.

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