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The sum of the areas of two circles is 80 pi

square meters. Find the length of the radius of each circle if one of them is twice as long as the other.

Verified Answer :

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The area of a circle is A = πr^2. We let A1 And A2 the areas of the circles and r1 and r2 the radius of each, respectivley.

A1 + A2 = 80π
Substitute the formula for the area,
π(r1)^2 + π (r2)^2 = 80π

From the statement, we know that r2=2(r1).

π(r1)^2 + π (2 x r1)^2 = 80π
We can cancel π, we will have

5 x (r1)^2 = 80
Thus,

r1 = 4 and r2 = 8

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