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, [tex] \frac{DN}{AR}=\frac{NS}{RH}=\frac{DS}{AH} [/tex]
Substituting the measurements of the corresponding sides.
[tex] \frac{72}{21.6}=\frac{NS}{RH}=\frac{110}{x} [/tex]
Equating the first and last ratio of the corresponding sides,
[tex] \frac{72}{21.6}=\frac{110}{x} [/tex]
Cross multiplying in the above equation, we get
[tex] 72 \times x = 110 \times 21.6 [/tex]
[tex] 72 \times x = 2376 [/tex]
[tex] x=\frac{2376}{72} [/tex]
x= 33.
Therefore, the value of x is 33.
