GED Mathematical Reasoning TestQuantitative Problem Solving with MeasurementMedium
A city engineer is planning a new pedestrian bridge. A support cable will run diagonally from the top of a 15-foot tower to a point on the ground 8 feet away from the base of the tower. What is the minimum length of the support cable needed, in feet?
- A25
- B23
- C13
- D17
Show answer & explanationAnswer & explanation
Correct answer: D. 17
This scenario forms a right-angled triangle where the tower height (15 feet) and the distance from the base (8 feet) are the legs, and the cable length is the hypotenuse. Using the Pythagorean theorem (a² + b² = c²): 8² + 15² = c². 64 + 225 = c². 289 = c². c = √289 = 17 feet.
Why the other options are wrong
- A. This is another common Pythagorean triple (7, 24, 25) but not for these dimensions, or a calculation error.
- B. This is the sum of the two legs (8 + 15) or a calculation error.
- C. This is a common Pythagorean triple (5, 12, 13) but not for these dimensions, or a calculation error.
Pythagorean Theorem
In a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (legs).
- Formula: a² + b² = c²
- Applies only to right triangles.
- Used to find an unknown side length when two are known.
Memory trick: Legs squared, then summed, for the hypotenuse's fame!