Question

In the figure shown , the lengths of segments AC , BC ,CD , are given in terms of the variable x . If AB Parallel to the DE , solve for x and determine if the dimensions are reasonable ?

Answer 1

• x=-6

,

• Not Reasonable, Length cannot be negative

Explanation:

In the given figure, the two triangles (ABC and DCE) are similar.

The ratio of corresponding sides is:

`\begin{gathered} (AC)/(CD)=(BC)/(CE) \\ \implies(x)/(x+2)=(x+3)/(x+4) \end{gathered}`

We solve for x:

`\begin{gathered} \begin{equation*} (x)/(x+2)=(x+3)/(x+4) \end{equation*} \\ \text{ Cross multiply} \\ x(x+4)=(x+2)(x+3) \\ \text{ Expand the brackets} \\ x^2+4x=x^2+3x+2x+6 \\ x^2+4x=x^2+5x+6 \\ x^2+5x+6-x^2-4x=0 \\ x+6=0 \\ x=-6 \end{gathered}`

The value of x is -6.

Since x is a negative number, the dimensions are not reasonable as length cannot be negative.