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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 ?

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 a class=

Respuesta :

Answer:

• 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:

[tex]\begin{gathered} \frac{AC}{CD}=\frac{BC}{CE} \\ \implies\frac{x}{x+2}=\frac{x+3}{x+4} \end{gathered}[/tex]

We solve for x:

[tex]\begin{gathered} \begin{equation*} \frac{x}{x+2}=\frac{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}[/tex]

The value of x is -6.

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

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