2019 · Q40
Let PQRS be a parallelogram whose diagonals PR and QS intersect at O. If △QRS is an equilateral triangle having a side of length 10 cm, then what is the length of the diagonal PR?
Elementary MathematicsQuadrilaterals and Polygons
- A5√3 cm
- B10√3 cm
- C15√3 cm
- D20√3 cm
Explanation
QS is a diagonal of the parallelogram and a side of equilateral triangle QRS, so half-diagonal QO = 5. The other diagonal PR = 2xRO, where RO is the altitude of the equilateral triangle = 5.sqrt(3). Hence PR = 10.sqrt(3) cm.