A homeowner is building a square fence around his circular patio so that each side of the fence is tangent to the circle, as sho
wn in the diagram below. The radius of his patio is 18 yards. What is the perimeter of his fence?
2 answers:
Answer: 144 yards
<u>Step-by-step explanation:</u>
Perimeter of a square (P) = 4s <em>where s is the side length of the square</em>
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.
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<h2>Answer: Lines b & c are parallel.⇄</h2>
Step-by-step explanation:
- When lines are perpendicular, the product of their slope is -1 (the slopes are negative reciprocal).
- When lines are parallel, they have the same slope.
Slope = ( y₂ - y₁) / (x₂ - x₁)
Slope of Line b = ( 6 - 1 ) ÷ ( 1 - 9 )
= 5 ÷ (- 8)
= - ⁵/₈
Slope of Line c = ( 12 - 7 ) ÷ ( 2 - 10 )
= - ⁵/₈
⇒ Line b ║ Line c