Question

Please help me I don’t know how to do this

Answer 1

3/2

Explanation:

Since it is an equilateral triangle, all sides are equal.

Which means that the line that crosses divides the side into two equal parts.

A right triangle is formed, therefore, using the Pythagorean theorems we can calculate the length of x, like this:

`\begin{gathered} c^2=a^2+b^2 \\ \text{ in this case:} \\ c=\sqrt[]{3} \\ a=\frac{\sqrt[]{3}}{2} \\ b=x \end{gathered}`

We substitute and solve for x, like this:

`\begin{gathered} \mleft(√(3)\mright)^2=\mleft((√(3))/(2)\mright)^2+x^2 \\ 3=(3)/(4)+x^2 \\ x=\sqrt[]{3-(3)/(4)} \\ x=\sqrt[]{(9)/(4)}=(3)/(2) \end{gathered}`

The value of x is 3/2