Given:
Figure of similar triangles.
To find:
The value of x and the measure of NR.
Solution:
In triangle RST and RMN,
[tex]\angle SRT\cong \angle MRN[/tex] (Vertically opposite angles)
[tex]\angle RST\cong \angle RMN[/tex] (Alternate interior angles)
[tex]\Delta RST\sim \Delta RMN[/tex] (By AA property of similarity)
We know that, corresponding sides of similar triangles are proportional.
[tex]\dfrac{RS}{RM}=\dfrac{RT}{RN}[/tex]
[tex]\dfrac{40}{8}=\dfrac{60}{2x-2}[/tex]
[tex]5=\dfrac{60}{2x-2}[/tex]
[tex]2x-2=\dfrac{60}{5}[/tex]
On further simplification, we get
[tex]2x=12+2[/tex]
[tex]x=\dfrac{14}{2}[/tex]
[tex]x=7[/tex]
The value of x is 7.
Now,
[tex]NR=2x-2[/tex]
[tex]NR=2(7)-2[/tex]
[tex]NR=14-2[/tex]
[tex]NR=12[/tex]
Therefore, the value of x is 7 and the measure of NR is 12 units.
