The value of h in the triangle is 6 units.
What is similar triangle?
Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. Similar triangles are the triangles that are the same in shape, but may not be equal in size.
For the given situation,
The triangles ΔNMP ~ ΔONP.
If two triangles are similar then the ratio of their sides are same.
⇒ [tex]\frac{NP}{MP} =\frac{OP}{NP}[/tex]
⇒ [tex]\frac{h}{12} =\frac{3}{h}[/tex]
⇒ [tex](h)(h)=(3)(12)[/tex]
⇒ [tex]h^{2} =36[/tex]
⇒ [tex]h=\sqrt{36}[/tex]
⇒ [tex]h=6[/tex]
Hence we can conclude that the value of h in the triangle is 6 units.
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