A Pythagorean triple gives three whole-number side lengths of a right triangle, so a familiar pair of legs can reveal the hypotenuse at once. First identify the side across from the right angle. If you don't recognize the triple, use the Pythagorean theorem and evaluate the square root in Desmos. For a missing hypotenuse, add the squares of the legs, not the legs themselves.
Hints
- Hint 1
The hypotenuse sits opposite the right angle and is always longer than either leg. Since you're given both legs, which side of a right-triangle triple are you trying to find?
- Hint 2
A Pythagorean triple has two smaller sides whose squares add to the largest side's square. The legs and are a familiar pair. Which third number completes their triple?
Step-by-step
Approach 1: Recognize the right-triangle triple
Step 1Identify the missing side
No Desmos needed. These side lengths belong to a familiar right-triangle triple.
The legs meet at the right angle; the hypotenuse is opposite it. So the length you want must be longer than , the longer given leg.
- Step 2
Complete the triple
The familiar Pythagorean triple is --: its leg squares fit . The largest number is the hypotenuse, so the triangle's hypotenuse is centimeters. Choice B.
Approach 2: Use the Pythagorean theorem
Step 1Write the equation for the hypotenuse
Let name the hypotenuse. The Pythagorean theorem says the leg squares add to the hypotenuse square, so:
- Step 2
Take the positive square root
A length is positive, so take the square root of both sides:
- Step 3
Evaluate the length
Type in Desmos. It prints , so the hypotenuse is centimeters. Choice B.