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Suppose the radius is R cm.

Then the perimeter of the rectangle is 2*(3+R) = 6 + 2R cm.

The length of the arc of the semicircle is pi*R and the length of the diameter is 2*R so the perimeter of the semicircle is pi*R + 2R

The two perimeters are equal so 6 + 2r = pi*R + 2R

That is, 6 = pi*R and so R = 6/pi

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Q: How do you find the radius of a semi circle with an equal perimeter to a rectangle with 1 side 3cm and the other side equal to the radius?
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