If the area of a circle is (4x 2 + 20x + 25)π, what is the diameter of the circle?

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Accepted Answer

The area of a circle is equal to πr 2 , where r is the radius of the circle. Therefore, the radius of this circle is equal to the square root of (4x 2 + 20x + 25). Factor this trinomial into 2 identical factors: (2x)(2x) = 4x 2 , (5)(5) = 25, and (2x)(5) + (2x)(5) = 20x. Therefore, (4x 2 + 20x + 25) = (2x + 5)(2x + 5), and the square root of (4x 2 + 20x + 25) is 2x + 5. The diameter of a circle is twice its radius, so the diameter of this circle is 2(2x + 5) = 4x + 10.

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