The perimeter of a semicircle is 25.7 kilometres. What is the semicircle's radius?
Question
Solution
The perimeter of a semicircle is given by the formula P = πr + 2r, where r is the radius of the semicircle.
Given that the perimeter P is 25.7 kilometres, we can set up the equation:
25.7 = πr + 2r
To solve for r, we first combine like terms:
25.7 = r(π + 2)
Then, we divide both sides by (π + 2) to isolate r:
r = 25.7 / (π + 2)
Using the approximation π ≈ 3.14, we find:
r ≈ 25.7 / (3.14 + 2) ≈ 25.7 / 5.14 ≈ 5 kilometres
So, the radius of the semicircle is approximately 5 kilometres.
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