Determine the length of the longest side of a right triangle if the lengths of the two other sides are six centimeters and eight centimeters.
So we are told that this is a right triangle. And it says to determine the length of the longest side of the right triangle. The longest side is always across from the 90-degree angle. And it says the two other sides are six centimeters and eight centimeters.
So if we’re wanting to find that length of that longest side, we can use the Pythagorean theorem. The Pythagorean theorem states: the sum of the squares of the shorter sides is equal to the square of the longest side.
So the two shorter sides are six and eight. And the longest side, we can let it be called 𝑥 so we have it equal to 𝑥 squared. So six squared is 36. Eight squared is 64. And then 𝑥 squared is simply 𝑥 squared.
So 36 plus 64 is 100. Now we need to square root both sides to isolate 𝑥. And the square root of 100 is 10. So this means the longest side would be 10 centimeters. Therefore, 10 centimeters will be our final answer.