Question

A quadrilateral PLAY is to be constructed with PL = 3 cm, LA = 4 cm, AY = 4.5 cm, PY = 2 cm. Which of the following value given for LY is not possible?

Answer 1

Since one side of a triangle cannot be greater than the sum of the other two sides, diagonal LY must be smaller than the sum of PL + PY (for triangle PLY) as well as AL + AY (for triangle ALY).
PL + PY = 5 and AL + AY = 8.5. Hence, LY must be less than 8.5 as well as 5.
Thus, the correct answer is 6.