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The rectangular game board below is 30 inches long and 20 inches wide. A shadedequilateral triangle is shown on the game board.20 in.10 in.30 in.If a player randomly drops a game piece on the game board, what is the probabilitythat the game piece will land on the shaded triangle?

Answer :

For this problem we use the formula for the area of an equilateral triangle

[tex]\begin{gathered} AT\text{ = }\frac{\sqrt[]{3}}{4}\cdot a^2\text{ = }\frac{\sqrt[]{3}}{4}(10in)^2\text{ = 25}\sqrt[]{3}in^2 \\ \end{gathered}[/tex]

Then, the probability that the piece lands on the triangles is the area of the triangle over the area of the reactangle

[tex]P=\frac{AT}{AR}=\text{ }\frac{25\sqrt[]{3}in^2}{30\cdot20in^2}=\frac{\sqrt[]{3}}{24}[/tex]

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