Radical Word Problems

Name:

Class:

Date:

Show your work for each problem.

1.
A ladder is 10 feet long. If it reaches 8 feet up a wall, how far is the base from the wall?
1. a)8 feet
2. b)4 feet
3. c)6 feet
4. d)5 feet
2.
A square garden has an area of 144 square meters. What is the side length?
3.
What formula would you use to find the diagonal of a rectangle with length 8 and width 6?
1. a)
2. b)
3. c)
4. d)
4.
A rectangular TV screen is 32 inches wide and 24 inches tall. Find the diagonal (screen size).
5.
Find the distance between points and .
6.
A square has an area of 72 square cm. What is the side length in simplest radical form?
1. a) cm
2. b) cm
3. c) cm
4. d) cm
7.
Find the distance between points and .
8.
A kite string is 25 meters long. The kite is directly above a point 7 meters from the person holding the string. How high is the kite?
9.
A baseball diamond is a square with 90-foot sides. What is the distance from home plate to second base? Give your answer in simplest radical form.
10.
A ramp rises 5 feet over a horizontal distance of 12 feet. How long is the ramp surface?
1. a)15 feet
2. b)17 feet
3. c)13 feet
4. d) feet
11.
A rectangular pool is 15 meters by 8 meters. A swimmer swims diagonally across. What is the exact distance?
12.
Find the distance between and . Express in simplest radical form.
13.
A 20-foot wire connects the top of a pole to a stake in the ground. If the stake is 16 feet from the base of the pole, how tall is the pole?
14.
Find the distance between and .
1. a)
2. b)
3. c)7
4. d)5
15.
A helicopter is hovering at a height . A rescue basket is lowered to a point 50 meters from directly below the helicopter. If the cable is 130 meters long, how high is the helicopter?
16.
A square has a diagonal of cm. What is the side length?