Question

Find the value of x.​

Answer 1

Answer:

$x=4$

Step-by-step explanation:

The two given triangles, triangle (BDE) and triangle (BAC) share the angle (<B) in common. Moreover, their bases, line (DE), and line (AC) are parallel, this means that through the corresponding angles postulate, angles (<BDE) and (<BAC) are congrunet. Moreover, angles (<BED) and (<BCA) are also congruent. Thus, triangles (BDE) and (BAC) are similar through angle-angle similarity.

The ratio between the corresponding sides of similar triangles is the same. Therefore, one can form the following equation,

$\frac{BD}{BA}=\frac{BE}{BC}$.

Substitute,

$\frac{BD}{BD+DA}=\frac{BE}{BE+EC}\\\\\frac{x+2}{x+x+2}=\frac{3}{3+2}$

Simplify,

$\frac{x+2}{2x+2}=\frac{3}{5}$

Cross products,

$5(x+2)=3(2x+2)$

Simplify, distribute, multiply every term inside the parenthesis by the term outside of it,

$5x+10=6x+6$

Inverse operations,

$5x+10=6x+6\\\\10=x+6\\\\4=x$