Question

The two triangles are similar.

Answer 1

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.

Answer 2

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.

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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.