$18 \cdot 28$ If the roots of the equations $2 x^{2}-18 x+36=0$ and $x^{2}-20 x+75=0$ are the lengths of four segments, then these segments
(A) can form a quadrilateral with a perimeter of 38.
(B) can form a quadrilateral with a perimeter of 29.
(C) cannot form a quadrilateral.
(D) none of the above.
(Chinese Jiangsu Province Junior High School Mathematics Competition, 1989)
[Solution] It is not difficult to find that the roots of the two equations are 3, 6 and 5, 15, respectively.
By $3+5+6=14<15$,
that is, one of the line segments is longer than the sum of the other three line segments, which clearly cannot form a quadrilateral. Therefore, the answer is $(C)$.