Explanation

Given the area A = 172.1 cm², and the formula for the area of a circle is A = πr²:

Step 1: Find the radius

172.1 = πr²

r² = 172.1 / π

r² = 172.1 / (22/7)

r² = 172.1 * (7/22)

r² = 54.77

r ≈ √54.77

r ≈ 7.4

Step 2: Calculate the circumference

Circumference C = 2πr

C = 2 * (22/7) * 7.4

C ≈ 2 * 3.14 * 7.4

C ≈ 46.51

Explanation

To simplify 5/(2 - √3), rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator (2 + √3):

Step 1: Multiply by the conjugate

(5 / (2 - √3)) * ((2 + √3) / (2 + √3))

= (5(2 + √3)) / ((2 - √3)(2 + √3))

Step 2: Simplify the denominator

(2 - √3)(2 + √3) = 2² - (√3)²

= 4 - 3

= 1

Step 3: Simplify the expression

(5(2 + √3)) / 1

= 10 + 5√3