# 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.

• Subject:

Mathematics
• Author:

laytonmcintosh
• Created:

7 months ago

x = 7

Step-by-step explanation:

For better understanding of the solution see the attached figure :

Given : AD = 6 units , BD = 8 units, m∠ABC = m∠DBE = 90° and               ∠DEB ≅ ∠ACB

Now, AB = AD + BD

= 8 + 6 = 14 units

In ΔABC and ΔDBE,

∠DBE = ∠ABC ( Each of 90° )

∠DEB = ∠ACB ( Both angles are congruent to each other )

So, By using AA postulate of similarity of triangles , ΔABC ~ ΔDBE

So, proportion of the corresponding sides will be equal.

\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

Hence, x = 7 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,

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

Therefore, the value of x is 7. x = 10 Explanation: Since the two triangles are similar, their corresponding sides are in proportion. Therefore, we can set up a proportion using the side lengths of the smaller triangle and the larger triangle and then solve for x. The corresponding sides have the following proportion: 2x - 2 : 3x = 6 : 8 We can then solve this proportion for x: 2x - 2 = 6 ; 3x = 8 2x = 8 ; x = 4 3x = 8 ; x = 10 Therefore, the value of x is 10.

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