Radical Word Problems

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
Answer: 6 feet
Using Pythagoras: , so , thus and feet.
2.
A square garden has an area of 144 square meters. What is the side length?
Answer: 12
Since Area , we have meters.
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)
Answer:
The diagonal is the hypotenuse of a right triangle, so we use Pythagorean Theorem: .
4.
A rectangular TV screen is 32 inches wide and 24 inches tall. Find the diagonal (screen size).
Answer: 40
1. What formula do we use? Pythagorean Theorem
2. Calculate 1024
3. Calculate 576
4. Add the squares: 1600
5. Take the square root: 40
5.
Find the distance between points and .
Answer: 5
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
Answer: cm
cm
7.
Find the distance between points and .
Answer: 10
1. Find (difference in x-coordinates) 6
2. Find (difference in y-coordinates) 8
3. Calculate 36
4. Calculate 64
5. Add: 100
6. Take square root: 10
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?
Answer: 24
Using : , so and meters.
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.
Answer: 90*sqrt(2)
1. What geometric shape connects home to second base? diagonal
2. Calculate 8100
3. For a square diagonal: . What is ? 16200
4. Simplify to simplest form 90*sqrt(2)
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
Answer: 13 feet
feet. This is the 5-12-13 Pythagorean triple!
11.
A rectangular pool is 15 meters by 8 meters. A swimmer swims diagonally across. What is the exact distance?
Answer: 17
1. Calculate 225
2. Calculate 64
3. Add: 289
4. What is ? 17
12.
Find the distance between and . Express in simplest radical form.
Answer: 5
. This is the 3-4-5 triangle!
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?
Answer: 12
1. The wire is 20 feet. This represents which part of the triangle? hypotenuse
2. Calculate 400
3. Calculate 256
4. For height: . Calculate 144
5. What is ? 12
14.
Find the distance between and .
1. a)
2. b)
3. c)7
4. d)5
Answer: 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?
Answer: 120
1. The cable (130 m) is which part of the triangle? hypotenuse
2. Calculate 16900
3. Calculate 2500
4. . Calculate 14400
5. What is ? 120
16.
A square has a diagonal of cm. What is the side length?
Answer: 10
Since , we have cm.