A triangle has a side of length 6 cm, a side of length 8 cm and a right angle. What is the shortest possible length of the remaining side of the triangle? Express your answer in centimeters as a decimal to the nearest hundredth.
Since the triangle is a right triangle, the hypoteneuse of the right triangle will be the longest side of the triangle. You are looking for the shortest side of the triangle. The Pythagorean Theorem says that \(c^2 = a^2 + b^2 \), where c is the length of the hypoteneuse. In this case, c=8 and you are looking for b. In this problem, it doesn't matter whether you call the shortest side "a" or "b", all you know for sure is that the shortest side isn't "c".
Therefore, \(8^2=6^2+b^2 or 64=36+b^2\). So,
\(b^2=64-36=28 \). Therefore b = Square Root of 28. rounded to the nearest hundreth is \(5.29 \).