Question

If an equilateral triangle has an altitude measuring 17 root 3 what is the measure of its sides?

Answer 1

The equilateral triangle has a side length of 34

Here, given the altitude of an equilateral triangle, we want to get the measure of its sides

Let the sides measure be x (all sides are equal)

The altitude divides the base length into two equal parts

So, one part of the base will measure x/2

So we have a right-angled triangle with hypotenuse x , while the two other sides are x/2 and 17 root 3

Using Pythagoras' theorem, we understand that the square of the hypotenuse equals the sum of the squares of the two other sides

Mathematically, we have this as follows;

`\begin{gathered} x^2\text{ = (17}\sqrt[]{3})^2\text{ + (}(x)/(2))^2 \\ \\ x^2\text{ = 867 + }(x^2)/(4) \\ \\ \text{Multiply through by 4} \\ \\ 4x^2=3468+x^2 \\ \\ 4x^2-x^2\text{ = 3468} \\ \\ 3x^2\text{ = 3468} \\ \\ x^2\text{ = }(3468)/(3) \\ \\ x^2\text{ = 1156} \\ \\ x^2=34^2 \\ \\ x\text{ = 34} \end{gathered}`