GED Mathematical Reasoning TestQuantitative Problem Solving with MeasurementMedium
A technician is installing a new antenna pole. To stabilize it, three guy wires are attached from the top of the 12-foot pole to points on the ground 5 feet from the base of the pole. What is the total length of the three guy wires needed?
- A39 feet
- B26 feet
- C45 feet
- D13 feet
Show answer & explanationAnswer & explanation
Correct answer: A. 39 feet
Each guy wire forms a right triangle with the pole and the ground. Use the Pythagorean theorem (a² + b² = c²) to find the length of one guy wire (hypotenuse). Then, multiply that length by 3 for the total length of all three wires.
Why the other options are wrong
- B. This is double the length of one guy wire, not three.
- C. This results from incorrect application of the Pythagorean theorem or multiplication.
- D. This is the length of only one guy wire, not three.
Pythagorean Theorem Application
Used to find the length of a side in a right-angled triangle when the lengths of the other two sides are known, often applied in real-world scenarios involving heights, distances, and diagonals.
- Formula: a² + b² = c²
- a and b are the lengths of the legs, c is the hypotenuse
- Useful for finding lengths in construction, navigation, etc.
Memory trick: Pole to Ground, Hypotenuse Found