Pythagorean Theorem

Show your work for each problem.

1.
In a right triangle, which side is always the longest?
1. a)The longer leg
2. b)They are all equal
3. c)The shorter leg
4. d)The hypotenuse
Answer: The hypotenuse
The hypotenuse is always the longest side of a right triangle. It's the side opposite the right angle (90°).
2.
The Pythagorean theorem states that . What does represent?
1. a)The area
2. b)The hypotenuse
3. c)One of the legs
4. d)The perimeter
Answer: The hypotenuse
In the Pythagorean theorem , represents the hypotenuse (the longest side), while and are the two legs.
3.
A right triangle has legs of length 3 and 4. What is the length of the hypotenuse?
Answer: 5
. Since , . This is the famous 3-4-5 right triangle!
4.
Calculate:
Answer: 169
. Notice that , so 5-12-13 is a Pythagorean triple!
5.
Find the hypotenuse of a right triangle with legs of length 6 and 8.
Answer: 10
1. What is ? 36
2. What is ? 64
3. What is ? 100
4. What is ? 10
6.
A right triangle has a hypotenuse of 13 and one leg of 5. Find the other leg.
Answer: 12
1. What is ? 169
2. What is ? 25
3. What is ? 144
4. What is ? 12
7.
Which set of numbers forms a Pythagorean triple?
1. a)7, 8, 9
2. b)5, 6, 7
3. c)4, 5, 6
4. d)8, 15, 17
Answer: 8, 15, 17
. The 8-15-17 triangle is a Pythagorean triple! The other options don't satisfy .
8.
A 10-meter ladder leans against a wall with its base 6 meters from the wall. How high does it reach?
Answer: 8
Using : , so , , meters.
9.
A ship sails 9 km east, then 12 km north. How far is it from its starting point?
Answer: 15
1. What is ? 81
2. What is ? 144
3. What is ? 225
4. What is ? 15
10.
A triangle has sides 6, 8, and 11. Is it a right triangle?
1. a)No, because 11 is odd
2. b)Yes, because
3. c)Yes, because it has three sides
4. d)No, because
Answer: No, because
Check: , but . Since , this is NOT a right triangle.
11.
Find the hypotenuse of a right triangle with legs 7 and 24.
Answer: 25
. The hypotenuse is 25. The 7-24-25 triangle is a famous Pythagorean triple!
12.
A rectangular TV screen is 48 inches wide and 36 inches tall. What is its diagonal size?
Answer: 60
1. What is ? 2304
2. What is ? 1296
3. What is ? 3600
4. What is ? 60
13.
A right triangle has a hypotenuse of 17 and one leg of 15. Find the other leg.
Answer: 8
1. What is ? 289
2. What is ? 225
3. What is ? 64
4. What is ? 8
14.
What is ?
Answer: 9
, so . Knowing perfect squares helps solve Pythagorean problems faster!
15.
A carpenter needs a diagonal brace for a frame that is 5 feet by 12 feet. How long should the brace be?
Answer: 13
1. What is ? 25
2. What is ? 144
3. What is ? 169
4. What is ? 13