SOLUTION: The diagonals of a parallelogram ABCD are perpendicular. If one diagonal has a length of 6 and the other diagonal has a length of 8, what is the perimeter of the parallelogram?
Algebra ->
Parallelograms
-> SOLUTION: The diagonals of a parallelogram ABCD are perpendicular. If one diagonal has a length of 6 and the other diagonal has a length of 8, what is the perimeter of the parallelogram?
Log On
Question 1143435: The diagonals of a parallelogram ABCD are perpendicular. If one diagonal has a length of 6 and the other diagonal has a length of 8, what is the perimeter of the parallelogram? Answer by ikleyn(52806) (Show Source):
If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
In this case, the diagonals divide the rhombus in four congruent right-angled triangles.
For each such a triangle, the legs are 6/2 = 3 units and 8/2 = 4 units;
hence, the sides of the rhombus are = 5 units long, and its perimeter is 5*4 = 20 units.
