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Perimeter, Ares, and VolumeIdentilying side lengths that give right trianglesDetermine whether a triangle with the given side lengths is a right triangle.\begin{tabular}{|l|c|c|c|}\hline \multicolumn{}{|c|}{ Side lengths } & Right triangle & \begin{tabular}{c} Not a right \\triangle\end{tabular} & \begin{tabular}{c} Not enough \\information\end{tabular} \\\hline (a) & & & \\\hline (b) & & & \\\hline (c) & & & \\\hline (d) & & & \\\hline\end{tabular}
Full solution
Q. Perimeter, Ares, and VolumeIdentilying side lengths that give right trianglesDetermine whether a triangle with the given side lengths is a right triangle.\begin{tabular}{|l|c|c|c|}\hline \multicolumn{}{|c|}{ Side lengths } & Right triangle & \begin{tabular}{c} Not a right \\triangle\end{tabular} & \begin{tabular}{c} Not enough \\information\end{tabular} \\\hline (a) & & & \\\hline (b) & & & \\\hline (c) & & & \\\hline (d) & & & \\\hline\end{tabular}
- Apply Pythagorean Theorem: To determine if a set of three side lengths forms a right triangle, we can use the Pythagorean theorem, which states that for a right triangle with legs a and b, and hypotenuse c, the following equation holds true: . We will apply this theorem to each set of side lengths.
- Check Set (a): For set (a) with side lengths , , and , we assume the longest side is the hypotenuse, so we check if .Calculating each term gives us .Adding the squares of the shorter sides, we get , which is equal to .Therefore, the set (a) does form a right triangle.
- Check Set (b): For set (b) with side lengths , , and , we check if .Calculating each term gives us .Adding the squares of the shorter sides, we get , which is not equal to .Therefore, the set (b) does not form a right triangle.
- Check Set (c): For set (c) with side lengths , , and , we check if .Calculating each term gives us .Adding the squares of the shorter sides, we get , which is equal to .Therefore, the set (c) does form a right triangle.
- Check Set (d): For set (d) with side lengths , , and , we check if .Calculating each term gives us .Adding the squares of the shorter sides, we get , which is not equal to .Therefore, the set (d) does not form a right triangle.
