Answer:
12
Step-by-step explanation:
A rhombus is a parallelogram with all four sides equal.
Its diagonals are perpendicular.
Each of the triangles formed by the diagonals and the sides are congruent, so the area of the rhombus is 4 times the area of one of the triangles.
Since the short diagonal is given as 4, each of the triangles can be viewed as having a base of 2. Each triangle's height, h, then is one half the length of the long diagonal.
The are of one of the triangles is 1/2 (base)(height)=(1/2)(2)h
The area of the rhombus is then
4(1/2)(2)h=24
Solving for h gives
h=6
This makes the length of the long diagonal 2h=12
