Digital SATMath: Geometry and TrigonometryEasy
A construction worker is installing a new window. The window frame is perfectly rectangular, and its diagonal measures 5 feet. If the height of the window is 3 feet, what is the width of the window?
- A2 feet
- B4 feet
- C8 feet
- D6 feet
Show answer & explanationAnswer & explanation
Correct answer: B. 4 feet
The window frame forms a right-angled triangle with its height, width, and diagonal. Using the Pythagorean theorem (a^2 + b^2 = c^2), where c is the diagonal, we can find the width.
Why the other options are wrong
- A. Incorrect. This would imply a shorter diagonal (sqrt(3^2+2^2) = sqrt(13) approx 3.6 feet).
- C. Incorrect. This would imply a much longer diagonal (sqrt(3^2+8^2) = sqrt(73) approx 8.5 feet).
- D. Incorrect. This would imply a longer diagonal (sqrt(3^2+6^2) = sqrt(45) approx 6.7 feet).
Pythagorean Theorem Application
The Pythagorean theorem (a^2 + b^2 = c^2) is used to find an unknown side of a right-angled triangle when two sides are known.
- Applies only to right-angled triangles.
- c always represents the hypotenuse (the longest side, opposite the right angle).
- a and b represent the other two sides (legs).
Memory trick: Right angle, right answer, sides squared, sum it up!