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Question
The sum of diameter of two circles is 112 cm and the sum of their areas is 5236 cm2 Find the radii of the two circles.
Solution
Sum of the diameters = 112 cm
Therefore, sum of the radii = `112/2` cm = 56 cm
If r is the radius of one circle, radius of other circle is (56 - r)
Sum of the areas = π r2 + π (56 - r)2
⇒ π r2 + π (56 - r)2 = 5236
⇒ π r2 + π (3136 - 112 r + r2) = 5236
⇒ (r2 + 3136 - 112 r + r2) × `22/7` = 5236
⇒ 2r2 - 112r + 3136 = 1666
⇒ 2r2 - 112r + 3136 - 1666 = 0
⇒ 2r2 - 112r + 1470 = 0
⇒ r2 - 56r + 735 = 0
⇒ (r - 35)(r - 21) = 0
⇒ r = 35 , r = 21
Therefore, radii of the two circles is 35 cm and 21 cm
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