.
The diagonals of a rhombus are 30 cms and 40 cm long.find its side.
~~~~~~~~~~~~~~~~~~~~~~
In any rhombus, the diagonals bisect each other and are perpendicular.
It is the characteristic property of a rhombus.
Therefore, the diagonals of a rhombus divide it in four congruent right-angled triangles.
For each of these triangles, the halves of diagonals are the legs, while the side of a rhombus is the hypotenuse of such a triangle.
So, you have right angled triangle with the legs = 15 cm and = 20 cm.
Hence, the side of the rhombus, which is the hypotenuse of the right angled triangle, is = = = 25 cm long.
Answer. The side of the rhombus is 25 cm long.
Solved.
-----------------
On basic properties of a rhombus see the lessons
- Diagonals of a rhombus are perpendicular
- Diagonals of a rhombus bisect its angles
- PROPERTIES OF RHOMBIS
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".