The distance around a circular dance hall room is 135 feet. What is the longest distance around the dance hall?

Answer: 43feet

Step-by-step explanation:

Perimeter = 135 feet

Since perimeter = 2πr

135 = 2πr

Recall that π = 3.14

135 = 2 * 3.14 * r

135 = 6.28 * r

135 = 6.28r

r = 135/6.28

r = 21.5

d = 2r

d = 2 * 21.5

d = 43 feet

42.95 feet

Step-by-step explanation:

In this question, we are tasked with calculating the distance around the dance hall that is the greatest.

Now, to answer this, we must have at the back of our mind that the dance hall is circular in shape. Thus, the greatest distance that could arise is the distance from one edge of the dance hall to the other end of the dance passing exactly through the center of the dance hall.

This distance described above is the diameter of the dance hall.

Notice we were given a length in the question? This length refers to the circumference around the circular dance hall.

Reframing then question, we were just told to calculate the diameter of a circle given the circumference of the circle.

Mathematically, circumference C of a circle = 2 * pi * r

Recall, mathematically also 2r = D

so we can say C = pi * D

Using the value of 22/7 for pi and the value of the circumference in the question, we have;

135 = 22/7 * D

D = (7 * 135) / 22

D = 42.95 feet