For a right triangle with whole-number sides, a Pythagorean triple can give the missing length quickly. Identify the hypotenuse, the side across from the right angle, and match it to the triple’s longest side. If you don’t recognize the triple, remember that the two legs’ squares, not their lengths, add to the hypotenuse’s square.
Hints
- Hint 1
The hypotenuse is across from the right angle and is always the longest side. Which given length must be the hypotenuse, and which is one of the two legs?
- Hint 2
A Pythagorean triple is three whole-number side lengths of a right triangle. The squares of the two shorter lengths add to the square of the longest. Do you know a triple containing both given lengths?
Step-by-step
Match a familiar right-triangle triple
Step 1Identify the longest side
No Desmos needed. A familiar right-triangle triple gives the missing length. The hypotenuse is across from the right angle and is longer than either leg, a side that forms the right angle. So the given centimeters is the hypotenuse.
- Step 2
Match the sides to the triple
The -- Pythagorean triple satisfies : the legs’ squares add to the hypotenuse’s square. You have the leg and the hypotenuse, so the other leg is centimeters. Match the longest side before using a triple. Choice C.