triangle abc is congruent to triangle xyz. in $ \triangle abc $, $ ab = 12 \mathrm { cm } $ and $ ac = 14 \mathrm { cm } $. in $ \triangle xyz $, $ yz = 10 \mathrm { cm } $ and $ xz = 14 \mathrm { cm } $.
what is the perimeter of $ \triangle abc $?
$ \bigcirc 36 \mathrm { cm } $
$ \bigcirc 38 \mathrm { cm } $
$ \bigcirc 40 \mathrm { cm } $
$ \bigcirc 50 \mathrm { cm } $

Question

Accepted Answer

# Explanation:
## Step1: Use congruent triangles property
Since $\triangle ABC\cong\triangle XYZ$, corresponding sides are equal. So $AB = XY = 12\mathrm{cm}$, $AC=XZ = 14\mathrm{cm}$, $BC = YZ=10\mathrm{cm}$.
## Step2: Calculate the perimeter of $\triangle ABC$
The perimeter $P$ of a triangle is $P=a + b + c$. For $\triangle ABC$, $P=AB + BC+AC$. Substitute $AB = 12\mathrm{cm}$, $BC = 10\mathrm{cm}$, $AC = 14\mathrm{cm}$ into the formula: $P=12 + 10+14$.
$$
\begin{align*}
P&=(12 + 14)+10\
&=26+10\
&=36
\end{align*}
$$

# Answer:
$36\mathrm{cm}$ (the first option)

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QUESTION IMAGE

Question

Explanation:

Step1: Use congruent triangles property

Step2: Calculate the perimeter of \(\triangle ABC\)

Answer: