Word Problems
Overview
Apply geometry concepts to real-world situations. These word problems require you to identify when to use the Pythagorean theorem and transformations to solve practical problems.
Practice Problems
Question 1: A rectangular park is 300 meters long and 400 meters wide. A jogger runs diagonally across the park. How far does she run?
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Answer: 500 meters
d^2 = 300^2 + 400^2 = 90000 + 160000 = 250000. d = 500 meters.
Question 2: A 17-foot ladder reaches a window 15 feet above the ground. How far is the base of the ladder from the wall?
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Answer: 8 feet
b^2 + 15^2 = 17^2. b^2 + 225 = 289. b^2 = 64. b = 8 feet.
Question 3: A robot starts at position (0, 0) and moves to (6, 8). What is the straight-line distance traveled?
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Answer: 10 units
d = sqrt(6^2 + 8^2) = sqrt(36 + 64) = sqrt(100) = 10 units.
Question 4: A photographer enlarges a 4x6 inch photo by a scale factor of 3. What are the new dimensions?
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Answer: 12 x 18 inches
Multiply each dimension by 3: 4 x 3 = 12 inches, 6 x 3 = 18 inches.
Question 5: A ship sails 5 km east, then 12 km north. How far is it from its starting point?
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Answer: 13 km
d^2 = 5^2 + 12^2 = 25 + 144 = 169. d = 13 km.
Question 6: A crane lifts a beam. The cable is 26 meters long and the beam is 10 meters from the base of the crane horizontally. How high is the beam lifted?
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Answer: 24 meters
h^2 + 10^2 = 26^2. h^2 + 100 = 676. h^2 = 576. h = 24 meters.
Question 7: An architect designs a building to be reflected across a street for a mirror-image twin building. If the original building's entrance is at (20, 15) and the street runs along y = 0, where is the twin's entrance?
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Answer: (20, -15)
Reflection over y = 0 (x-axis) keeps x the same and negates y: (20, 15) becomes (20, -15).
Question 8: A TV screen is advertised as 65 inches (diagonal). If the screen is 52 inches wide, what is its height?
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Answer: 39 inches
h^2 + 52^2 = 65^2. h^2 + 2704 = 4225. h^2 = 1521. h = 39 inches.
Question 9: A map has a scale where 1 cm represents 5 km. A park shown as 3 cm x 4 cm on the map has what actual dimensions?
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Answer: 15 km x 20 km
Scale factor is 5: 3 x 5 = 15 km, 4 x 5 = 20 km.
Question 10: A baseball diamond is a square with 90-foot sides. How far must a catcher throw from home plate to second base?
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Answer: Approximately 127.3 feet
The throw is along the diagonal: d^2 = 90^2 + 90^2 = 8100 + 8100 = 16200. d = sqrt(16200) = 127.3 feet.