The value of x is 7 in both similar triangles.
Given that the two triangles are similar. The attachment shows the triangles.
[tex]\Delta MNP[/tex] is equivalent to [tex]\Delta OPR[/tex]. Also, [tex]\angle MPN[/tex] is equal to [tex]\angle OPR[/tex] and both are right angles. Also given that,
NO = 6, NP = 8, MP = 2x-2, PR = 3x
Thus, OP = NO + NP
OP = 6+8= 14
As per the AA postulate of similarity theorem of triangles, the corresponding sides will be equal.
[tex]\dfrac {OP}{NP} = \dfrac {PR}{MP} =\dfrac {OR}{MN}[/tex]
We take the two sides,
[tex]\dfrac {OP}{NP} = \dfrac {PR}{MP}[/tex]
[tex]\dfrac {14}{8} = \dfrac {3x}{2x-2}[/tex]
[tex]28x-28 = 24x[/tex]
[tex]4x = 28[/tex]
[tex]x = 7[/tex]
Hence we can conclude that the value of x is 7.
To know more about the AA postulate of similarity theorem, follow the link given below.
https://brainly.com/question/2820198?referrer=searchResults
