Question

It is proposed to build a single circular park equal in area to the sum of area of 2 circular park of radius of 16m and 12m in a locality.Find the radius of new park.

Answer 1

ar. of first circle = pie × r ^2.
= 22/7 × 16^2
= 22/7 × 256
= 804.57m^2

similarly , ar of second circle with radius 12 m= 452.57m^2

Now,
804.57 + 452.57 = Pie × r ^ 2

= > 1257.14 = pie × r ^2
= > 1257.14 = 22/7 × r ^ 2

= > 1257.14× 7 /22 = r^2

= > 399.99 = r^2

SO ,
r = root 399.99
= 19.99 m...... ( exact)
or
20m............. ( approx.)

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Answer 2

Given that the area of the required circular park = areas of 2 circular parks
Let radius of required park be R. 
sum of areas of 2 parks $\pi$(16$x^{2}$+12$x^{2}$)
area of new park=$\pi$R$x^{2}$
 On equating, R$x^{2}$=144+256
therefore, R = root of 400=20m