Question:
The lengths of the diagonals of a rhombus are 30 cm and 40 cm. Find the side of the rhombus.
Solution:
GIVEN: the lengths of the diagonals of a rhombus are 30 cm and 40 cm.
TO FIND: side of the rhombus.
Let the diagonals AC and CD of the rhombus ABCD meet at point O.
We know that the diagonals of the rhombus bisect each other perpendicularly.
Hence in right triangle AOD, by Pythagoras theorem
hypotenuse $^{2}=$ perpendicular $^{2}+$ base $^{2}$
$=15^{2}+20^{2}$
$=225+400$
$=625$
hypotenuse $=25 \mathrm{~cm}$
Hence the side of the rhombus is $=25 \mathrm{~cm}$