Question

Given that the triangles are similar, find the value of x. Find the length of NR.

Answer 1

Given:

Figure of similar triangles.

To find:

The value of x and the measure of NR.

Solution:

In triangle RST and RMN,

$\angle SRT\cong \angle MRN$              (Vertically opposite angles)

$\angle RST\cong \angle RMN$              (Alternate interior angles)

$\Delta RST\sim \Delta RMN$                 (By AA property of similarity)

We know that, corresponding sides of similar triangles are proportional.

$\dfrac{RS}{RM}=\dfrac{RT}{RN}$

$\dfrac{40}{8}=\dfrac{60}{2x-2}$

$5=\dfrac{60}{2x-2}$

$2x-2=\dfrac{60}{5}$

On further simplification, we get

$2x=12+2$

$x=\dfrac{14}{2}$

$x=7$

The value of x is 7.

Now,

$NR=2x-2$

$NR=2(7)-2$

$NR=14-2$

$NR=12$

Therefore, the value of x is 7 and the measure of NR is 12 units.