Answer:
(D)7 in.
Step-by-step explanation:
A regular hexagon can be divided into six equilateral triangles.
Therefore:
[tex]b=\dfrac{c}{2}[/tex]
Applying Pythagoras Theorem
[tex]c^2=12^2+b^2\\c^2=12^2+(\frac{c}{2})^2\\c^2-(\frac{c}{2})^2=12^2\\c^2-\dfrac{c^2}{4}=144\\\dfrac{4c^2-c^2}{4}=144\\\dfrac{3c^2}{4}=144\\$Cross multiply\\3c^2=144 \times 4\\3c^2=576\\$Divide both sides by 3\\c^2=192\\$Therefore:\\c=\sqrt{192}\\c=8\sqrt{3}$ in.[/tex]
Recall that b=c/2
Therefore:
[tex]b=4\sqrt{3} \approx 7$ in.[/tex]
The value of b is 7 inches.
