Question

What is the length of DE

Answer 1

The answer is b.6, you set up a proportion of the corresponding sides in both triangles...12/9=8/x solve for x and get 6.

Answer 2

Answer:

The correct option is B.

Step-by-step explanation:

Given information: XY=9, YZ=12, XZ=12, DE=x, EF=8, DF=8, ∠Z=44°, ∠F=44°.

In triangle XYZ and DEF,

$\angle Z=\angle F=44^{\circ}$               (Given)

$\frac{XZ}{YZ}=\frac{12}{12}=1$

$\frac{DF}{EF}=\frac{8}{8}=1$

$\frac{XZ}{YZ}=\frac{DF}{EF}$

Since two corresponding sides are proportions and their included angle is same, therefore triangle XYZ and DEF are similar.

Corresponding sides of similar triangles are proportional.

$\frac{XY}{DE}=\frac{YZ}{EF}$

$\frac{9}{x}=\frac{12}{8}$

$\frac{9}{x}=\frac{3}{2}$

On cross multiplication we get

$9\times 2=3x$

$18=3x$

Divide both sides by 3.

$6=x$

The length of DE is 6 units. Therefore the correct option is B.