Question

In the figure shown, the lenghts of segments AC, BC, and CE are given in terms of the variable x.If AB || DE, solve for x and determine is the dimensions are reasonable? Justify your answer.Neter your answer and your justification in the space provined.It is an OPENENDED!Please do the exercise work, I need it !! Thank you!

Answer 1

SOLUTION

In this question,

We have that AC = x,

BC = x + 3,

CE = x + 4,

CD = x + 2

Using similar triangles, we have that:

$\frac{AC}{CD}\text{ = }\frac{BC}{CE}$

$\begin{gathered} \frac{x}{x\text{ + 2}}\text{ = }\frac{x\text{ + 3}}{x\text{ + 4}} \\ \\ \text{cross - multiply, we have that : } \\ \text{ x ( x + 4 ) = ( x + 3 ) ( x + 2 )} \\ x^2+4x=x^2\text{ + 5x + 6} \\ 4\text{ x - 5x = 6} \\ -\text{ x = 6} \\ \text{x = -6} \\ \end{gathered}$

CONCLUSION: The dimensions are not reasonable.