It is known that the bottom surface ABCD of a pyramid p-abcd is a square with side length 1, PD ⊥ bottom surface ABCD, and BD = 2. If the point G is on the line PA, and the volume of the pyramid g-pbc is one fourth, the length of the line PG is calculated

It is known that the bottom surface ABCD of a pyramid p-abcd is a square with side length 1, PD ⊥ bottom surface ABCD, and BD = 2. If the point G is on the line PA, and the volume of the pyramid g-pbc is one fourth, the length of the line PG is calculated

It should be PD = 2. (equal volume method) from the title, PA = radical 5, VP ACD = 1 / 3, VC ABP = 1 / 3, VG PBC = 1 / 4, VC ABG = 1 / 12, so pg / Ag = 3 (the same height and different base of area method), solid Ag = 1 / 4 times radical 5, PG = 3 / 4 times radical 5