What is the diameter of a circle whose area is equal to the sum of the areas of two circles of diameter 10 cm and 24 cm?
Given:
Let the two circles be C1 and C2 with diameters 10 cm and 24 cm respectively.
Area of circle, C = Area of C1 + Area of C2 …… (i)
∵ Diameter = 2 × radius
∴ Radius of C1, r1 = 
= 5 cm
and Radius of C2, r2 = 
= 12 cm
∵ Area of circle = πr2 …… (ii)
∴ Area of C1 = πr12
= 
= 
= 
cm2
Similarly, Area of C2 = πr22
= 
= 22/7 × 144
= 
cm2
∴ Using equation (i), we have
Area of C = 
+ 
= 
cm2
Now, using equation (ii), we have
× r2 = 
r2 = 
r2 = 169
r = 
r = 13 cm
⇒ Diameter = 2 × r
= 2 × 13
= 26 cm
Hence, the diameter of the circle is 26 cm.
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