Question 1189499
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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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<pre>
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

    {{{sqrt(10^2 + 24^2)}}} = {{{sqrt(100 + 576)}}} = {{{sqrt(676)}}} = 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.



<U>ANSWER</U>.  The perimeter of the rhombus is  4*26 = 104 meters.
</pre>

Solved.


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On rhombis, see the lessons in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Parallelograms/Diagonals-of-a-rhombus-are-perpendicular.lesson>Diagonals of a rhombus are perpendicular</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Parallelograms/Diagonals-of-a-rhombus-bisect-its-angles.lesson>Diagonals of a rhombus bisect its angles</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/The-length-of-diagonals-of-a-rhombus.lesson>The length of diagonals of a rhombus</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/A-circle-inscribed-to-the-rhombus.lesson>A circle inscribed in the rhombus</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/How-to-solve-problems-on-the-rhombus-sides-and-diagonals-measures-Examples.lesson>HOW TO solve problems on the rhombus sides and diagonals measures - Examples</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/The-length-of-diagonals-of-a-rhombus.lesson>The length of diagonals of a rhombus</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Parallelograms/PROPERTIES-OF-RHOMBIS.lesson>PROPERTIES OF RHOMBIS</A>


Also, &nbsp;you have this free of charge online textbook on Geometry

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson>GEOMETRY - YOUR ONLINE TEXTBOOK</A> 

in this site.


The referred lessons are the part of this textbook under the topic "<U>Properties of rhombis</U>".



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.