triangle ABC is congruent to triangle XYZ. In ΔABC, AB = 12 cm and AC = 14 cm. In △XYZ, YZ = 10 cm and XZ = 14 cm. What is the perimeter of ΔABC?

Use ratios.

AC is in the same place as XZ.

Put them over each other. Put two ther sides over each other. In this case, we don't know the side that goes with AB so we're trying to find it.

[tex] \frac{14}{14} = \frac{12}{?} [/tex]
Cross multiply. (Bottom 14 by the twelve divided by the top 14.)

You get 12. Side XY is 12.

Normally, you'd do the same to find side BC, but it's already obvious the sides equal each other. BC = 10

Add ABC's sides to find the perimeter.

[tex]14 + 12 + 10 = {?}[/tex]
Your answer is 36.

Hope this helps!

:)

MrRoyal MrRoyal · Answer 2 · 2021-11-03T12:37:04+01:00

Congruent triangles have equal measures.

The perimeter of ΔABC is 36 cm

The given parameters are:

[tex]\mathbf{\triangle ABC \cong \triangle XYZ}[/tex]

So, we have:

[tex]\mathbf{AB =XY = 12}[/tex]

[tex]\mathbf{AC =XZ = 14}[/tex]

[tex]\mathbf{BC =YZ = 10}[/tex]

So, the perimeter of ΔABC is:

[tex]\mathbf{Perimeter = AB + AC + BC}[/tex]

This gives

[tex]\mathbf{Perimeter = 12 + 14 + 10}[/tex]

[tex]\mathbf{Perimeter = 36}[/tex]

Hence, the perimeter of ΔABC is 36 cm

Read more about congruent triangles at:

https://brainly.com/question/22062407