ANSWER:
3/2
STEP-BY-STEP 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:
[tex]\begin{gathered} c^2=a^2+b^2 \\ \text{ in this case:} \\ c=\sqrt[]{3} \\ a=\frac{\sqrt[]{3}}{2} \\ b=x \end{gathered}[/tex]
We substitute and solve for x, like this:
[tex]\begin{gathered} \mleft(\sqrt{3}\mright)^2=\mleft(\frac{\sqrt{3}}{2}\mright)^2+x^2 \\ 3=\frac{3}{4}+x^2 \\ x=\sqrt[]{3-\frac{3}{4}} \\ x=\sqrt[]{\frac{9}{4}}=\frac{3}{2} \end{gathered}[/tex]
The value of x is 3/2
