Question

△ABC is similar to △XYZ. Also, side AB measures 6 cm, side BC measures 18 cm, and side XY measures 12 cm.

Answer 1

Answer: YZ=36 cm

Step-by-step explanation:

Given: △ABC is similar to △XYZ.

Side AB =6 cm, side BC = 18 cm, and side XY=12 cm.

We know that if two triangles are similar then their sides are proportional.

Therefore, if △ABC is similar to △XYZ.

Then, $\frac{AB}{XY}=\frac{BC}{YZ}$

$\\\Rightarow\frac{6}{12}=\frac{18}{YZ}\\\Rightarrow\ YZ=\frac{18\times12}{6}\\\Rightarrow\ YZ=36\ cm$

Answer 2

Answer:

value of sides YZ is 36 cm

Step-by-step explanation:

Similar triangles states that the length of the corresponding sides are in proportion.

Given that: ΔABC is similar to ΔXYZ

then;

Corresponding sides are in proportion i.e

$\frac{AB}{XY}=\frac{BC}{YZ}=\frac{AC}{XZ}$    .....[1]

As per the statement:

side AB = 6 cm, side BC =18 cm and side XY = 12 cm.

Substitute these in [1] to solve for side YZ;

$\frac{6}{12}= \frac{18}{YZ}$

or

$\frac{1}{2} = \frac{18}{YZ}$

By cross multiply we have;

$YZ = 36$ cm

Therefore, the value of sides YZ is 36 cm