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lyudmila [28]
3 years ago
13

**BRAINLIEST IF ANSWERED***

Mathematics
1 answer:
goblinko [34]3 years ago
6 0

Answer:

(D)7 in.

Step-by-step explanation:

A regular hexagon can be divided into six equilateral triangles.

Therefore:

b=\dfrac{c}{2}

Applying Pythagoras Theorem

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.

Recall that b=c/2

Therefore:

b=4\sqrt{3} \approx 7$ in.

The value of b is 7 inches.

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