As shown in the figure, e is the point on the diagonal BD of the square ABCD with side length 1, be = BC, P is any point on CE, PQ ⊥ BC is at point Q, PR ⊥ be is at point R, then the value of PQ + PR is () A. 22B. 12C. 32D. 23

As shown in the figure, e is the point on the diagonal BD of the square ABCD with side length 1, be = BC, P is any point on CE, PQ ⊥ BC is at point Q, PR ⊥ be is at point R, then the value of PQ + PR is () A. 22B. 12C. 32D. 23

Connect BP, make cm ⊥ BD through C, ∵ s △ BCE = s △ BPE + s △ BPC = BC × PQ × 12 + be × PR × 12 = BC × (PQ + PR) × 12 = be × cm × 12, BC = be, ∵ PQ + PR = cm, ∵ be = BC = 1 and the square diagonal BD = 2BC = 2, BC = CD, cm ⊥ BD, ∵ m is the midpoint of BD, and ⊥ BDC is the right triangle