Digital SATMath: Geometry and TrigonometryEasy
A carpenter is building a wooden frame for a window. The frame is rectangular, with a width of 30 inches and a height of 40 inches. To ensure the frame is perfectly square, the carpenter measures the diagonal. What should be the length of the diagonal?
- A50 inches
- B60 inches
- C35 inches
- D70 inches
Show answer & explanationAnswer & explanation
Correct answer: A. 50 inches
The diagonal of a rectangle forms the hypotenuse of a right-angled triangle with the width and height as its legs. Using the Pythagorean theorem (a² + b² = c²), where a=30 and b=40, we find c=50.
Why the other options are wrong
- B. This is an incorrect calculation, possibly adding the sides or other miscalculation.
- C. This is an incorrect calculation, possibly an average or other miscalculation.
- D. This is an incorrect calculation, possibly multiplying by a factor or other miscalculation.
Pythagorean Theorem
In a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (legs).
- Applies only to right-angled triangles.
- Formula: a² + b² = c², where 'c' is the hypotenuse.
- Used to find unknown side lengths when two sides are known.
Memory trick: Right triangles always follow the 'A-Squared-Plus-B-Squared-Equals-C-Squared' rule.