Question

Find the value of x.​

Answer 1

`x=4`

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,

`(BD)/(BA)=(BE)/(BC)`.

Substitute,

`(BD)/(BD+DA)=(BE)/(BE+EC)\\\\(x+2)/(x+x+2)=(3)/(3+2)`

Simplify,

`(x+2)/(2x+2)=(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`