In an equilateral triangle, the difference between the circumradius and the inradius is 3 cm. Find the area.
27√3 cm2
For an equilateral triangle of side \(a\), the circumradius is \(R = \frac{a}{\sqrt{3}}\) and the inradius is \(r = \frac{a}{2\sqrt{3}}\).
So \(R - r = \frac{a}{\sqrt{3}} - \frac{a}{2\sqrt{3}} = \frac{a}{2\sqrt{3}}\).
Given \(R - r = 3\), so \(\frac{a}{2\sqrt{3}} = 3 \Rightarrow a = 6\sqrt{3}\) cm.
Area of an equilateral triangle is \(\frac{\sqrt{3}}{4}a^2 = \frac{\sqrt{3}}{4}\times(6\sqrt{3})^2 = \frac{\sqrt{3}}{4}\times108 = 27\sqrt{3}\) cm2.
The area of the triangle is 27√3 cm2.
Important Questions from Properties of Triangles
What is the perimeter of the triangle ?
Consider the following statements :
1. ABC is right angled triangle
2. The angles of the triangle are in AP
Which of the statements given above is/are correct ?
What is the nature of the triangle ?
If c = 8, what is the area of the triangle ?
What is the value of n ?
