2020 · Q78
ABCD is a parallelogram where AC and BD are the diagonals. If ∠BAD = 60°, ∠ADB = 90°, then what is BD² equal to?
Elementary MathematicsQuadrilaterals and Polygons
- A(3/5)AB²
- B(3/4)AB²
- C(1/2)AB²
- D(2/3)AB²
Explanation
In △ABD, ∠BAD = 60° and ∠ADB = 90°, so ∠ABD = 30°. Then BD = AB·sin60° = AB√3/2, giving BD² = 3AB²/4. For example, with AB = 2 the diagonal BD is √3.