2015 · Q88
The diagonals of a trapezium are at right angles, and the slant sides, if produced, form an equilateral triangle with the greater of the two parallel sides. If the area of the trapezium is 16 square cm, then the distance between the parallel sides is
Elementary MathematicsQuadrilaterals and Polygons
- A2 cm
- B4 cm
- C8 cm
- DCannot be determined due to insufficient data
Explanation
The extended slant sides form an equilateral triangle, so the trapezium is isosceles with u = (b−a)/2; perpendicular diagonals give h² = ((a+b)/2)², so h = (a+b)/2; area (a+b)h/2 = (a+b)²/4 = 16 gives a+b = 8 and h = 4 cm (option B).