the perimeter of $\triangle abc$ is 13 cm. it was dilated to create $\triangle abc$. what is the perimeter…

the perimeter of $\triangle abc$ is 13 cm. it was dilated to create $\triangle abc$. what is the perimeter of $\triangle abc$? 13 cm 26 cm 39 cm 52 cm

the perimeter of $\triangle abc$ is 13 cm. it was dilated to create $\triangle abc$. what is the perimeter of $\triangle abc$? 13 cm 26 cm 39 cm 52 cm

Answer

Answer:

39 cm

Explanation:

Step1: Find the scale - factor

The scale - factor $k$ of the dilation is found by comparing the lengths of corresponding segments. Given $OB = 5$ and $OB'=5 + 15=20$, so $k=\frac{OB'}{OB}=\frac{20}{5}=3$.

Step2: Use the property of perimeter in dilation

When a figure is dilated by a scale - factor $k$, the perimeter of the dilated figure is $k$ times the perimeter of the original figure. The perimeter of $\triangle ABC$ is $P = 13$ cm. The perimeter of $\triangle A'B'C'$ is $P'=k\times P$. Substituting $k = 3$ and $P = 13$ cm, we get $P'=3\times13 = 39$ cm.