Question

Given that ABC ~ DEC. find the value of x. Write the equation and show your work.

Answer 1

From the problem, given triangle ABC is similar to triangle DEC, we can have the proportion of :

`(AB)/(AC)=(DE)/(DC)`

AB = 30, AC = 2x - 1

DE = 18, DC = x + 1

This will be :

`\begin{gathered} (30)/(2x-1)=(18)/(x+1) \\ \text{Cross multiply :} \\ 30(x+1)=18(2x-1) \\ 30x+30=36x-18 \\ 30x-36x=-18-30 \\ -6x=-48 \\ x=(-48)/(-6)=8 \end{gathered}`

The answer is x = 8