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.Com
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(52817)   (Show Source): You can put this solution on YOUR website!
.

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.

Solved.

---------------

On relevant properties of rhombuses, see the lessons
    - Diagonals of a rhombus are perpendicular
    - Diagonals of a rhombus bisect its angles
    - The length of diagonals of a rhombus
    - HOW TO solve problems on the rhombus sides and diagonals measures - Examples
in this site.

Also,  you have this free of charge online textbook on Geometry
    GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.

The referred lessons are the part of this textbook under the topic "Properties of rhombis".


Save the link to this online textbook together with its description

Free of charge online textbook in GEOMETRY
https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson

to your archive and use it when it is needed.



RELATED QUESTIONS

A parallelogram has two diagonals which bisect each other. One diagonal has a length of... (answered by fractalier)
The area of a kite varies jointly with the lengths of its two diagonals. If a kite with... (answered by Mathtut)
The area of a kite varies jointly with the lengths of its two diagonals. If a kite with... (answered by josmiceli)
A rhombus has sides of length 6 cm. One of its diagonals is 10 cm long. Find the length... (answered by midwood_trail)
A kite has a 5-inch side and a 7-inch side. One of the diagonals is bisected by the... (answered by greenestamps)
A side and a diagonal of a parallelogram are 12 inches and 19 inches respectively. The... (answered by Edwin McCravy)
Two side of a parallelogram are 694 feet and 418 feet respectively, one diagonal is 602 (answered by Edwin McCravy,ikleyn)
a parallelogram with sides 12cm,8cm with one of the diagonal 10cm,find the length of... (answered by drk)
a kite of area 252 has one diagonal of length 9m.Find the length oof the other... (answered by addingup)