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14. The lengths of the diagonals of a rhombus is

    \[\mathbf{24cm}\text{ }\mathbf{and}\text{ }\mathbf{10cm}.\]

Find each side of the rhombus.
CBSE | Class 10 | Maths | RD Sharma | Triangles
14. The lengths of the diagonals of a rhombus is

    \[\mathbf{24cm}\text{ }\mathbf{and}\text{ }\mathbf{10cm}.\]

Find each side of the rhombus.

Solution:

Let ABCD be a rhombus and AC and BD be the diagonals of ABCD.

So, AC =

    \[24cm\text{ }and\text{ }BD\text{ }=\text{ }10cm\]

 

    \[\]

We know that diagonals of a rhombus bisect each other at right angle. (Perpendicular to each other)

So,

    \[AO\text{ }=\text{ }OC\text{ }=\text{ }12cm\text{ }and\text{ }BO\text{ }=\text{ }OD\text{ }=\text{ }3cm\]

    

    \[\]

In ∆AOB, by Pythagoras theorem, we have

    \[\begin{array}{*{35}{l}} <!-- /wp:paragraph --> <!-- wp:paragraph --> A{{B}^{2~}}=\text{ }A{{O}^{2}}~+\text{ }B{{O}^{2}} \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> =\text{ }{{12}^{2}}~+\text{ }{{5}^{2}} \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> =\text{ }144\text{ }+\text{ }25 \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> =\text{ }169 \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \Rightarrow AB\text{ }=\text{ }\surd 169\text{ }=\text{ }13cm \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \end{array}\]

                                                       

    \[\]

Since, the sides of rhombus are all equal.

Therefore, AB = BC = CD = AD =

    \[13cm.\]

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