Final answer:
To find the radius x of a semicircle with a perimeter of 80 cm, the formula P = πr + 2r is used. Solving for r, we find that r ≈ 80 / (π + 2), which gives r ≈ 15.56 cm.
Step-by-step explanation:
Calculating the Radius from the Perimeter of a Semicircle
To calculate x, which is the radius of a semicircle with a known perimeter, we need to use the formula for the perimeter of a semicircle:
P = πr + 2r
Since the perimeter P is given as 80cm, we can set up the equation:
80 = πr + 2r
This equation includes both π, the mathematical constant approximately equal to 3.14159, and r, the radius of the semicircle we are trying to find. Solving for r gives:
r(π + 2) = 80
r = 80 / (π + 2)
By calculating the numerator and the denominator, we can solve for the value of r:
r ≈ 80 / (3.14159 + 2)
r ≈ 80 / 5.14159
r ≈ 15.56 cm
Hence, the radius x of the semicircle is approximately 15.56 cm.