The value of [tex]\text{x}[/tex] is [tex]\boxed{x = 7}.[/tex]
Further Explanation:
The similar triangles are those in which all the corresponding angles are equal and the sides are proportional.
Explanation:
The [tex]\Delta {\text{ABC}}[/tex] and [tex]\Delta {\text{EBD}}[/tex] are similar to each other. Therefore, the ratios of the corresponding sides are equal.
The ratio of corresponding sides can be expressed as follows,
[tex]\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}[/tex]
Further solve the above equation.
[tex]\begin{aligned}\frac{7}{4} &= \frac{{3x}}{{2x - 2}}\\14x - 14 &= 12x\\14x - 12x &= 14\\2x&= 14\\x&= 7\\\end{aligned}[/tex]
The value of [tex]\text{x}[/tex] is [tex]\boxed{x = 7}.[/tex]
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, congruent triangle, similarity theorem, SSS congruency theorem, SSS similarity theorem, AA similarity postulate, SAS congruency postulate.
