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The lengths of the diagonals of a rhombus are 20 and 48 meters. What is the perimeter of the rhombus?
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In any rhombus, diagonals bisect each other and are perpendicular.
THEREFORE, the diagonals divide a rhombus into four congruent right-angled triangles.
Consider any of these triangle. Its legs are half-diagonals.
In our case, the legs of the considered triangle are 20/2 = 10 and 48/2 = 24 meters long.
Apply the Pythagorean theorem and calculate the hypotenuse length. It is
= = = 26 meters.
The hypotenuse is the side of the rhombus.
So, each side is 26 meters long.
Hence, the perimeter of the rhombus is 4*26 = 104 meters.
ANSWER. The perimeter of the rhombus is 4*26 = 104 meters.
Solved.
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On rhombis, see the lessons in this site
- Diagonals of a rhombus are perpendicular
- Diagonals of a rhombus bisect its angles
- The length of diagonals of a rhombus
- A circle inscribed in the rhombus
- HOW TO solve problems on the rhombus sides and diagonals measures - Examples
- The length of diagonals of a rhombus
- PROPERTIES OF RHOMBIS
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.