A Pythagorean triple is a set of whole-number side lengths for a right triangle. When you’re given a leg and the hypotenuse, check whether they fit a familiar pattern such as --. Match the hypotenuse to the longest side, then scale every side by the same factor. Subtracting the given lengths directly does not find a leg.
Hints
- Hint 1
The hypotenuse is the longest side of a right triangle. In the -- pattern, is the hypotenuse. Which side of the pattern matches the given -centimeter hypotenuse?
- Hint 2
A scale factor tells you what to multiply every side by. Compare and with and . What factor turns both pattern lengths into the given lengths?
Step-by-step
Use a scaled 3-4-5 triangle
Step 1Match the given sides to the pattern
No Desmos needed. These sides fit a scaled -- right triangle.
The hypotenuse is the side across from the right angle and is the longest side. So the given -centimeter hypotenuse matches in the pattern, while the -centimeter leg matches .
- Step 2
Find the scale factor
Both matches give the same scale factor, the number each pattern side is multiplied by:
- Step 3
Scale the remaining leg
The remaining leg in the pattern is , so multiply it by the same scale factor:
Subtracting from gives , but a leg is not the difference between the other two side lengths. The triangle’s other leg is centimeters. Choice B.