If the area of a circle is equal to the sum of the areas of two circles of diameters 10 cm and 24 cm, then diameter of the large circle (in cm) is

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KollegeApply · Accepted Answer

Let the diameter of the larger circle be d Now, Area of larger circle = Area of circle having diameter 10 cm + Area of circle having diameter 24 cm \Rightarrow $\pi$ \left( d/2 \right)^2 = $\pi$ \left( $\frac{10}{2}$ \right)^2 + $\pi$ \left( $\frac{24}{2}$ \right)^2 \Rightarrow \left( d/2 \right)^2 = \left( 5 \right)^2 + \left( 12 \right)^2 \Rightarrow \left( d/2 \right)^2 = 25 + 144 \Rightarrow \left( d/2 \right)^2 = {13}^2 \Rightarrow d/2 = 13 \Rightarrow d = 26 cm

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