The sum of the radii of two circles is 84 cm and the difference of their areas is 5544 cm². Calculate the radii of the two circles.
Mensuration
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The sum of the radii of two circles is 84 cm and the difference of their areas is 5544 cm2. Calculate the radii of the two circles.

KnowledgeBoat · Accepted Answer

Let r1 and r2 be the radii of the two circles. Given, Sum of the radii of two circles is 84 cm. r1 + r2 = 84 .......(1) Given, Difference of their areas is 5544 cm2. Area of circle1 - Area of circle2 = 5544 ⇒ πr12 - πr22 = 5544 ⇒ (r12 - r22) = 5544 ⇒ r12 - r22 = ⇒ r12 - r22 = ⇒ r12 - r22 = 1764 ⇒ (r1 + r2) (r1 - r2) = 1764 Substituting the value from equation (1) in above equation, we get : ⇒ 84(r1 - r2) = 1764 ⇒ r1 - r2 = ⇒ r1 - r2 = 21 ......(2) Adding equation (1) and (2), we get : ⇒ r1 + r2 + r1 - r2 = 84 + 21 ⇒ 2r1 = 84 + 21 ⇒ 2r1 = 105 ⇒ r1 = = 52.5 cm Substituting value of r1 in equation (1), we get : ⇒ r1 + r2 = 84 ⇒ 52.5 + r2 = 84 ⇒ r2 = 84 - 52.5 ⇒ r2 = 31.5 cm. Hence radii of the two circles = 52.5 cm and 31.5 cm.

Mathematics

The sum of the radii of two circles is 84 cm and the difference of their areas is 5544 cm². Calculate the radii of the two circles.

Mensuration

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