Math CentralQuandaries & Queries


Question from Sarah, a student:

The perimeter of a semicircle is doubled when the radius is increased by 7. Find the radius of the semicircle.

Hi Sarah,

Since this question mentions the perimeter of a semicircle we would like to find a formula for such an object. The perimeter is composed of two parts; the diameter of the circle (d=2*r) and half the circumference of a full circle (pi*r). Thus, P = (2+pi)*r is a general formula for the perimeter of a semicircle of radius 'r'. The question states that P is doubled (2*P) when radius is increased by 7 (r+7), thus 2*P = (2+pi)*(r+7). We have two equations in two unknowns, so we can use these to solve for 'r'. What do you notice about your solution? Can you make a general statement?


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