A homeowner is building a square fence around his circular patio so that each side of the fence is tangent to the circle, as shown in the diagram below. The radius of his patio is 18 yards. What is the perimeter of his fence?

144 yards

Step-by-step explanation:

The tangents will form a square of each side equal to the diameter.

Diameter = 2 × 18 = 36

Perimeter = 4×36 = 144 yards

144 yards

Step-by-step explanation:

Perimeter of a square (P) = 4s where s is the side length of the square

Since the fence is tangent (touching and perpendicular) to the patio, then the side length of the fence is the diameter of the circle. (See attachment)

Radius of circle = 18  ---> Diameter of circle = 2(18) = 36 ---> side length = 36

P = 4s

  = 4(36)

  = 144

NOTE: Whenever you have a word problem, ALWAYS draw a picture!

It will help you understand how to put together the information you are given in order to solve for the missing information.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."