Given △DNS∼△ARH. (Refer to the attached image)
When triangles are similar, then the ratio all three pairs of corresponding sides are equal.
Since, △DNS∼△ARH
Therefore, ![\frac{DN}{AR}=\frac{NS}{RH}=\frac{DS}{AH}](https://tex.z-dn.net/?f=%20%5Cfrac%7BDN%7D%7BAR%7D%3D%5Cfrac%7BNS%7D%7BRH%7D%3D%5Cfrac%7BDS%7D%7BAH%7D%20)
Substituting the measurements of the corresponding sides.
![\frac{72}{21.6}=\frac{NS}{RH}=\frac{110}{x}](https://tex.z-dn.net/?f=%20%5Cfrac%7B72%7D%7B21.6%7D%3D%5Cfrac%7BNS%7D%7BRH%7D%3D%5Cfrac%7B110%7D%7Bx%7D%20)
Equating the first and last ratio of the corresponding sides,
![\frac{72}{21.6}=\frac{110}{x}](https://tex.z-dn.net/?f=%20%5Cfrac%7B72%7D%7B21.6%7D%3D%5Cfrac%7B110%7D%7Bx%7D%20)
Cross multiplying in the above equation, we get
![72 \times x = 110 \times 21.6](https://tex.z-dn.net/?f=%2072%20%5Ctimes%20x%20%3D%20110%20%5Ctimes%2021.6%20)
![72 \times x = 2376](https://tex.z-dn.net/?f=%2072%20%5Ctimes%20x%20%3D%202376%20)
![x=\frac{2376}{72}](https://tex.z-dn.net/?f=%20x%3D%5Cfrac%7B2376%7D%7B72%7D%20)
x= 33.
Therefore, the value of x is 33.