Chapter 11, Problem 3PT

To determine

To Compute : The perimeter and area of triangle ABC.

Answer to Problem 3PT

The perimeter of triangle ABC is 6a mm and area of triangle ABC is $\sqrt{3}{a}^2$cm².

Explanation of Solution

Given information :

  

  $△ABC$ is an equilateral triangle with AC = BC = AB = 2a mm,

Let l be length of one side of the triangle. Then,

Perimeter of a equilateral triangle = 3l .

Therefore,

  $\text{Perimeter of}(△ABC)=3\times 2a=6a\text{}mm$ .

And,

Area of an equilateral triangle = $\frac{\sqrt{3}}{4}{l}^2$

That is, l = 2a mm

Therefore,

  $\text{Area}\text{of}(△ABC)=\frac{\sqrt{3}}{4}{(2a)}^2$

  $=\sqrt{3}{a}^{2}mm$.

Thus,

The perimeter of triangle ABC is 6a mm and area of triangle ABC is $\sqrt{3}{a}^2$cm².