Subject:
MathematicsAuthor:
laytonmcintoshCreated:
7 months agoAnswer:
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
Author:
jessietrda
Rate an answer:
8The 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.
Author:
angelinep1jv
Rate an answer:
3Rate an answer:
0Don't worry! There are several alternative approaches you can try to resolve your query. Here are some tips to help you find answers in different ways:
Remember, the process of finding answers often involves persistence, creativity, and an open mind. By exploring various resources, reaching out to others, and being proactive in your search, you increase your chances of finding the information you need. Happy quest for knowledge!