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A rectangular tile has a thin diagonal line drawn in its design. The longer dimension of the tile is 12 inches. The angle formed by the diagonal and the shorter side of the tile is 72°.

What is the perimeter of the tile?

 

Enter your answer, rounded to the nearest inch, in the box.

 

I got the answer 31.8 cm  rounded to the nearest inch..

AngelRay  Jun 11, 2018
 #1
avatar+19810 
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A rectangular tile has a thin diagonal line drawn in its design. The longer dimension of the tile is 12 inches. The angle formed by the diagonal and the shorter side of the tile is 72°.

What is the perimeter of the tile?

Enter your answer, rounded to the nearest inch, in the box.

 

Let s = shorter side.

 

\(\begin{array}{|rcll|} \hline \tan(72^{\circ}) &=& \dfrac{12}{s} \\ s &=& \dfrac{12}{\tan(72)^{\circ}} \\ s &=& \dfrac{12}{3.07768353718} \\\\ s &=& 3.89903635479 \\ \hline \end{array}\)


\(s = 3.89903635479\ \text{inch}\)

 

The perimeter of the tile is:

\(\begin{array}{|rcll|} \hline && 2\times 12 + 2\times 3.89903635479 \\ &=& 24 + 7.79807270959 \\ &=& 31.7980727096\ \text{inches} \\ \hline \end{array}\)

 

The perimeter of the tile rounded to the nearest inch is 32 inch.

 

laugh

heureka  Jun 11, 2018

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