GED Mathematical Reasoning TestQuantitative Problem Solving with MeasurementMedium
A construction worker needs to determine the length of a diagonal brace for a rectangular gate. The gate is 8 feet tall and 6 feet wide. What is the length of the diagonal brace?
- A14 feet
- B10 feet
- C12 feet
- D7 feet
Show answer & explanationAnswer & explanation
Correct answer: B. 10 feet
The diagonal brace forms the hypotenuse of a right-angled triangle, with the gate's height and width as the legs. Use the Pythagorean theorem: a² + b² = c². So, 6² + 8² = c² → 36 + 64 = c² → 100 = c² → c = 10 feet.
Why the other options are wrong
- A. This is the sum of the width and height, not the diagonal.
- C. This is twice the width, or an incorrect application of the theorem.
- D. Incorrect calculation; perhaps an average or simple sum error.
Pythagorean Theorem
In a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
- Applies only to right-angled triangles.
- Formula: a² + b² = c².
- Used to find an unknown side length when two sides are known.
Memory trick: Pythagoras helps find the longest side of a right triangle.