The sum of the areas of two circles is80π square meters. find the length of a radius of each circle if one of them is twice as long as the other what is the radius of the larger circle

Given Information

Area of 2 circles = 80π m²
One radius is twice as long as the other


Define Radius

Let one of the radius be x
Radius₁ = x
Radius₂ = 2x ← (Because it is twice as long)


Formula

Area of circle = πr²


Substitute the radius into the formula

Area of big circle + Area of small circle = πr₁² + πr₂²

Area of big circle + Area of small circle = πx² + π(2x)²

πx² + π(2x)² = 80π

πx² + π4x² = 80π


Divide by π through

x² + 4x² = 80
5x² = 80


Divide by 5 through

x² = 80 ÷ 5
x² = 16


square root both sides

x = √16
x = 4 (-4 is rejected, because length cannot be negative)


Find Radius

Radius₁ = x = 4m
Radius₂ = 2 = 2(4) = 8m


The radius of the smaller circle is 4m and the radius of the bigger circle is 8m.

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