GED Mathematical Reasoning TestQuantitative Problem Solving with MeasurementMedium
A plumber needs to run a pipe diagonally across a rectangular room. The room is 12 feet long and 5 feet wide. What is the shortest possible length of the pipe?
- A15 feet
- B13 feet
- C17 feet
- D10 feet
Show answer & explanationAnswer & explanation
Correct answer: B. 13 feet
The diagonal pipe forms the hypotenuse of a right-angled triangle, with the room's length and width as the legs. Use the Pythagorean theorem: a² + b² = c². So, 5² + 12² = c² → 25 + 144 = c² → 169 = c² → c = 13 feet.
Why the other options are wrong
- A. Incorrect calculation, possibly a sum of 5 and 10 or other error.
- C. This is the sum of the length and width (5+12).
- D. Incorrect calculation, possibly an average or sum error.
Pythagorean Triples
Sets of three positive integers a, b, and c, such that a² + b² = c².
- Common triples include (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25).
- Knowing these can quickly solve Pythagorean theorem problems.
- Any multiple of a triple is also a Pythagorean triple (e.g., 6, 8, 10).
Memory trick: Pythagorean triples are like special codes for right triangles.