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 hypotenuse
2. b)They are all equal
3. c)The longer leg
4. d)The shorter leg
2.
The Pythagorean theorem states that $a^2 + b^2 = c^2$ . What does $c$ represent?
1. a)The area
2. b)One of the legs
3. c)The hypotenuse
4. d)The perimeter
3.
A right triangle has legs of length 30 and 40. What is the length of the hypotenuse?
4.
Calculate: $5^2 + 12^2 = ?$
5.
Find the hypotenuse of a right triangle with legs of length 6 and 8.
6.
A right triangle has a hypotenuse of 26 and one leg of 10. Find the other leg.
7.
Which set of numbers forms a Pythagorean triple?
1. a)8, 15, 17
2. b)4, 5, 6
3. c)7, 8, 9
4. d)5, 6, 7
8.
A 5-meter ladder leans against a wall with its foot 1.4 meters from the wall. How high up the wall does it reach, in meters?
9.
A ship sails 16 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 $6 + 8 > 11$
3. c)Yes, because it has three sides
4. d)No, because $6^2 + 8^2 \neq 11^2$
11.
Find the hypotenuse of a right triangle with legs 20 and 21.
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 $\sqrt{81}$ ?
15.
A wooden garden gate is a rectangle 120 cm wide and 50 cm tall. How long, in cm, is the diagonal brace that runs from one corner to the opposite corner?