Answer:
x = 6.9 (option D)
Explanation:
Given:
DC = 4, CA = 7
CE = x, BA = x + 12
To find:
the value of x
To determine x, we will apply the similarity theorem for triangles:
For two triangles to be similar, the ratio of corresponding sides will be equal
Triangle EDC is similar to triangle BDA
[tex]\begin{gathered} DC\text{ corresponds to DA} \\ CE\text{ corresponds to AB} \\ \\ The\text{ ratio:} \\ \frac{DC}{DA}\text{ = }\frac{CE}{AB} \end{gathered}[/tex][tex]\begin{gathered} DA\text{ = DC +}CA \\ DA\text{ = 4 + 7 = 11} \\ \\ substitute\text{ the values:} \\ \frac{4}{11}=\frac{x}{x\text{ + 12}} \\ cross\text{ multiply:} \\ 4(x\text{ + 12\rparen = 11\lparen x\rparen} \\ 4x\text{ + 48 = 11x} \end{gathered}[/tex][tex]\begin{gathered} collect\text{ like terms:} \\ 48\text{ = 11x - 4x} \\ 48\text{ = 7x} \\ \\ divide\text{ both sides by 7:} \\ \frac{48}{7}\text{ = }\frac{7x}{7} \\ x\text{ = 6.857} \\ \\ x\text{ = 6.9 \lparen1 decimal place\rparen \lparen option D\rparen} \end{gathered}[/tex]
