Given that the triangles are similar, find the value of x. Find the length of NR. S
T
40
60
R
2x-2
8
N
M M
X
NR =

Given:

Figure of similar triangles.

To find:

The value of x and the measure of NR.

Solution:

In triangle RST and RMN,

             (Vertically opposite angles)

             (Alternate interior angles)

                (By AA property of similarity)

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

On further simplification, we get

The value of x is 7.

Now,

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

yes

\

step-by-step explanation:

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15