Suggested languages for you:

Americas

Europe

Problem 535

Show that the perimeter of an equilateral triangle which is inscribed in a circle with radius of length \(\mathrm{r}\) is \(3 \sqrt{3} \mathrm{r}\).

Expert verified

The short answer to the question is that when an equilateral triangle is inscribed in a circle of radius r, its perimeter can be calculated by first splitting the triangle into two 30-60-90 right triangles by dropping a perpendicular from a vertex to the base. Using the Pythagorean theorem and the properties of those right triangles, the side length of the equilateral triangle is found to be \(\sqrt{3} r/2\). Then, by multiplying this side length by 3, the perimeter of the triangle is found to be \(3\sqrt{3} r\).

What do you think about this solution?

We value your feedback to improve our textbook solutions.

- Access over 3 million high quality textbook solutions
- Access our popular flashcard, quiz, mock-exam and notes features
- Access our smart AI features to upgrade your learning

Chapter 28

Find the perimeter of a regular polygon of n sides inscribed in a circle of radius \(\mathrm{r}=10\) when \(\mathrm{n}\) equals: a) \(3 ; \mathrm{b}\) ) \(4 ;\) c) \(6 ;\) d) \(9 ;\) e) \(12 ;\) f \(18 ; \mathrm{g}\) ) 36 h) Find the circumference of the circle using \(\pi=3.14\); i) Comparing the answers to parts (a) through (g) with the answer to (h), what conclusion do you reach?

Chapter 28

Prove that the perimeter of a regular polygon of n sides which is inscribed in a circle of radius \(\mathrm{r}\) is given by \(P=2 \mathrm{nr} \sin (\pi / n)\)

Chapter 28

Show that for a triangle of area \(\mathrm{A}\), and perimeter \(\mathrm{P}\), the radius of the inscribed circle, \(\mathrm{r}\), equals $2 \mathrm{~A} / \mathrm{P}$.

Chapter 28

A regular hexagon is inscribed in a circle. If the length of the radius of the circle is 7 in. find the perimeter of the hexagon.

Chapter 28

Find the perimeter of a regular polygon of \(\mathrm{n}\) sides which is circumscribed about a circle of radius length 10 when \(\mathrm{n}\) equals a) \(3 ;\) b) \(4 ;\) c) \(6 ;\) d \(9 ;\) e) \(12 ;\) f) \(18 ;\) g) 36 .

The first learning app that truly has everything you need to ace your exams in one place.

- Flashcards & Quizzes
- AI Study Assistant
- Smart Note-Taking
- Mock-Exams
- Study Planner