Hello from MrBillDoesMath!
Answer:
Perimeter = 60
Height = 18/5
Discussion:
The diagonals of a rhombus bisect each other at right angles. So a rhombus can be viewed as the union of 4 congruent right triangles, each with legs (1/2)*18 = 9 and (1/2) *24 = 12. See attachment. This gives a hypotenuse length of 15 so the Perimeter = 4 *c = 60.
The height ( = altitude) of a rhombus is
= area / length of base
= (1/2) ( (18) * 24) /c
= (1/2) ( 18 * 24) / 60
= 18/5
Thank you,
MrB
