Since you're given opposite vertices and information about the lengths of the diagonals, it is probably useful to know some things about specific quadrilaterals. Kites—quadrilaterals where two consecutive sides are congruent and the other two (consecutive) sides are congruent—have perpendicular diagonals. Parallelograms have diagonals that bisect each other (that intersect at their midpoints). Rhombi (rhombuses) are simultaneously kites and parallelograms, which gives you some information about the diagonals of the rhombus in your particular problem.