Chapter 13.4, Problem 4MRE

To determine

To find the length of an altitude of an equilateral triangle.

Answer to Problem 4MRE

The length of an altitude of an equilateral triangle is $\sqrt{3}a$ .

Explanation of Solution

Given information:The lengths of one side of an equilateral triangle is 2a.

Calculation: The required length of an altitude of an equilateral triangle is obtained as,

From given data, obtained a figure,

  

In triangle BMC,

  $\begin{array}{l}\angle CMB={90}^0\\ BM=a\\ BC=2a\\ C{M}^2+M{B}^2=B{C}^2\\ C{M}^2=B{C}^2-M{B}^2\\ C{M}^2={\left(2a\right)}^2-a^2\\ C{M}^2=3a^2\\ CM=\sqrt{3}a\end{array}$

Hence, the length of an altitude of an equilateral triangle is $\sqrt{3}a$ .