Question

the length of the diagonals of a rhombus are 24 cm and 18 cm respectively find the length of the each side of the Rhombus

Answer 1

√9*9+12*12=√225
=side of rhombus is 15

Answer 2

Draw a rhombus of ABCD .
AC=24
BD=18
let the point of intersection of diagonal AC and BD be O.
$ao = \frac{1}{2} \times ac \\ ao = \frac{1}{2} \times 24 \\ ao = 12 \\ bo = \frac{1}{2} \times bd \\ bo = \frac{1}{2} \times 18 \\ bo = 9$
In Triangle AOB, it is a right angle triangle

${ab}^{2} = {ao}^{2} + {bo}^{2} \\ {ab}^{2} = {12 }^{2} + {9}^{2} \\ {ab}^{2} = 144 + 81 \\ {ab}^{2} = 225 \\ ab = \sqrt{225} \\ ab = 15$
length of rhombus is 15