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Kaylis [27]
3 years ago
15

The two triangles are similar.

Mathematics
2 answers:
Neko [114]3 years ago
7 0

Given that the triangles are similar.

When triangles are similar, all three pairs of corresponding sides are in the same ratio.

Similarly in the given triangles, the ratio of the corresponding sides are equal.

\frac{8}{2x-2}= \frac{8+6}{3x}

\frac{8}{2x-2}= \frac{14}{3x}

Cross multiplying, we get

8 \times 3x = 14 \times (2x-2)

24x = 28x-28

-4x = -28

Dividing both sides of the equation by -4.

So, we get

x = 7.

lina2011 [118]3 years ago
5 0

The value of x is \boxed{x = 7}.

Further Explanation:

Given:

The triangles are similar

Explanation:

The similar triangles are those in which all the corresponding angles are equal and the sides are proportional.

The \Delta {\text{ABC}} and \Delta {\text{EBD}} are similar to each other. Therefore, the ratios of the corresponding sides are equal.

The ratio of corresponding sides can be expressed as follows,

\begin{aligned}\frac{{{\text{AB}}}}{{{\text{EB}}}} &= \frac{{{\text{BC}}}}{{{\text{BD}}}} \\\frac{{{\text{AE}} + {\text{EB}}}}{{{\text{EB}}}} &= \frac{{{\text{BC}}}}{{{\text{BD}}}} \\\frac{{6 + 8}}{8}&= \frac{{3x}}{{2x - 2}}\\\frac{{14}}{8}&= \frac{{3x}}{{2x - 2}}\\\end{aligned}

Further solve the above equation.

\begin{aligned}\frac{7}{4} &= \frac{{3x}}{{2x - 2}}\\14x - 14 &= 12x\\14x - 12x &= 14\\2x &= 14\\x&= 7\\\end{aligned}

The value of x is \boxed{x = 7}.

Kindly refer to the image attached.

Learn more:

  1. 1.If the clothing maker bought 500 m2 of this fabric, how much money did he lose? use 1tepiz=0.625dollar and 0.9144m=1yard brainly.com/question/2479097.
  2. 2.Suppose that you find the volume of all the oceans to be 1.4×109km3 in a reference book. to find the mass, you can use the density of water, also found in this reference book, but first you must convert the volume to cubic meters. what is this volume in cubic meters? brainly.com/question/1446243.

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Triangle

Keywords: congruent, angles, triangle, ASA, angle side angle, congruent sides, acute angle, side, corresponding angles, value of x, two similar triangles, two triangles, similar.

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Step-by-step explanation:

The diagram is attached in the answer.

As both the angles are equal thus the two forms isosceles triangles. This is true because the converse of base angle theorem is applicable here. The theorem clearly states that when a trapezoid is divided by the diagonal, it forms two set of angles where m<1=m<2 and m<lmk=m<nmk

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