A prism whose side edge is perpendicular to the bottom is called a straight prism. It is known that the bottom is a rhombic straight prism. Its volume diagonals are 9 and 15 respectively, and its height is 5

A prism whose side edge is perpendicular to the bottom is called a straight prism. It is known that the bottom is a rhombic straight prism. Its volume diagonals are 9 and 15 respectively, and its height is 5


As shown in the figure, in abcd-a'b'c'd ', the two diagonals are a'c = 15cm, BD' = 9cm, and the side edges are AA '= DD' = 5cm. Both ∵ BDD 'and ∵ ACA' are right triangles. According to Pythagorean theorem, ac2 = 152-52 = 200, BD2 = 92-52 = 56, AC = 200 = 102, BD = 56 = 214 ∵