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There is a mistake in this question. The sum of the areas of two circles should be 52 π cm² instead of 52 cm².
Let the radius of one circle be x cm
Then, the radius of the other circle will be (10 - x) cm
Area of circle = πr²
⇒ πx² + π(10 - x)² = 52π
⇒ πx² + π(100 - 20x + x²) = 52π
Dividing it by π, we get.
⇒ x² + x² - 20x + 100 - 52 = 0
⇒ 2x² - 20x + 48 = 0
Dividing it by 2, we get.
⇒ x² - 10x + 24 = 0
⇒ x² - 6x - 4x + 24 = 0
⇒ x(x - 6) - 4(x - 6) = 0
⇒ (x - 4) (x - 6) = 0
x = 4 or x = 6
So, radii of two circles are 4 cm and 6 cm respectively.
There is a mistake in this question. The sum of the areas of two circles should be 52 π cm² instead of 52 cm².
Let the radius of one circle be x cm
Then, the radius of the other circle will be (10 - x) cm
Area of circle = πr²
⇒ πx² + π(10 - x)² = 52π
⇒ πx² + π(100 - 20x + x²) = 52π
Dividing it by π, we get.
⇒ x² + x² - 20x + 100 - 52 = 0
⇒ 2x² - 20x + 48 = 0
Dividing it by 2, we get.
⇒ x² - 10x + 24 = 0
⇒ x² - 6x - 4x + 24 = 0
⇒ x(x - 6) - 4(x - 6) = 0
⇒ (x - 4) (x - 6) = 0
x = 4 or x = 6
So, radii of two circles are 4 cm and 6 cm respectively.
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