Pythagorean Theorem

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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
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
3.
A right triangle has legs of length 3 and 4. What is the length of the hypotenuse?
4.
Calculate:
5.
Find the hypotenuse of a right triangle with legs of length 6 and 8.
6.
A right triangle has a hypotenuse of 13 and one leg of 5. Find the other leg.
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
8.
A 10-meter ladder leans against a wall with its base 6 meters from the wall. How high does it reach?
9.
A ship sails 9 km east, then 12 km north. How far is it from its starting point?
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
11.
Find the hypotenuse of a right triangle with legs 7 and 24.
12.
A rectangular TV screen is 48 inches wide and 36 inches tall. What is its diagonal size?
13.
A right triangle has a hypotenuse of 17 and one leg of 15. Find the other leg.
14.
What is ?
15.
A carpenter needs a diagonal brace for a frame that is 5 feet by 12 feet. How long should the brace be?