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Licemer1 [7]
2 years ago
5

The diagram shows a hexagon-shaped tile used for flooring. Each hexagon tile has an area of 18/3 in 2 Find x.​

Mathematics
2 answers:
mylen [45]2 years ago
7 0

Answer:

x = 12

Step-by-step explanation:

The hexagonal tile given here is made up of 6 triangles with equal bases and heights.

So, area of hexagonal tile will be equal to 6 times the area of one triangle.

Therefore,

18 \sqrt{3}  = 6 \times  \frac{1}{2}  \times 2 {( \sqrt{3)} }^{ \frac{x}{12} } . {( \sqrt{3)} }^{ \frac{x}{6} }  \\  \\ 18 \sqrt{3}  = 6  {( \sqrt{3)} }^{ \frac{x}{12} } . {( \sqrt{3)} }^{ \frac{2x}{12} }  \\  \\  \frac{18 \sqrt{3}  }{6}  = {( \sqrt{3)} }^{ \frac{x}{12}  +  \frac{2x}{12} }  \\  \\ 3 \sqrt{3}  =  {( \sqrt{3)} }^{ \frac{3x}{12} } \\  \\ 3. {3}^{ \frac{1}{2} }  =  {3}^{ \frac{3x}{24} }  \\  \\  {3}^{1 +  \frac{1}{2} }  =  {3}^{ \frac{x}{8} }  \\  \\ {3}^{ \frac{3}{2} }  =  {3}^{ \frac{x}{8} }  \\ (bases \: are \: equal \: so \: exponents \:  \\ will \: also \: be \: equal) \\ \implies  \frac{3}{2}  =  \frac{x}{8}  \\  \\ x =  \frac{3 \times 8}{2}  \\  \\ x = 3 \times 4 \\  \\ x = 12

alexira [117]2 years ago
7 0

Answer: x=12

Step-by-step explanation:

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