The two triangles are similar. What is the value of x? Enter your answer in the box. x = Two right triangles, one smaller than the other, back to back, so that their right angles form a straight angle. The two acute angles along the straight angle are congruent to each other. The overlapping part of the legs is labeled 8. The part of the overlapping side that extends above the smaller triangle is labeled 6. The leg of the smaller triangle that is a ray of the straight angle is labeled 2 x minus 2. The leg of the larger angle that is a ray of the straight angle is labeled 3 x.

[tex]\implies \frac{AB}{DB}=\frac{BC}{BE}=\frac{AC}{DE}\\\\\implies \frac{AB}{DB}=\frac{BC}{BE}\\\\\implies \frac{14}{8}=\frac{3\cdot x}{2\cdot x-2}\\\\\implies 28\cdot x-28=24\cdot x\\\implies 4\cdot x=28\\\implies x=7[/tex]

Hence, x = 7

aksnkj aksnkj · Answer 2 · 2021-11-15T06:46:59+01:00

The two triangles are similar. The value of x is 7.

Given information:

Two right triangles, one smaller than the other, back to back, so that their right angles form a straight angle.

The two triangles are similar.

The overlapping part of the legs is labeled 8. The part of the overlapping side that extends above the smaller triangle is labeled 6. The leg of the smaller triangle that is a ray of the straight angle is labeled 2x-2. The leg of the larger triangle that is a ray of the straight angle is labeled 3x. See the figure attached for more information.

The ratio of sides of triangles will be equal.

The ratio of the height of two triangles will be equal to the ratio of the base of them.

So, the value of x can be calculated as,

[tex]\dfrac{2x-2}{3x}=\dfrac{8}{8+6}\\\dfrac{2x-2}{3x}=\dfrac{4}{7}\\14x-14=12x\\2x=14\\x=7[/tex]

Therefore, the value of x is 7.

For more details, refer to the link:

https://brainly.com/question/14926756