Question

card 12
triangle rst is dilated using a scale factor of 1/4 to create triangle rst.
fill in the missing side lengths.

Explanation:

Step1: Recall dilation formula

If a figure is dilated with a scale - factor $k$, the length of a side of the dilated figure $l'$ and the length of the corresponding side of the original figure $l$ are related by $l'=k\times l$.

Step2: Find missing side - lengths of dilated triangle

Given the scale factor $k = \frac{1}{4}$. Let the side - lengths of the original triangle be $l_1$, $l_2$, $l_3$ and the side - lengths of the dilated triangle be $l_1'$, $l_2'$, $l_3'$.
If one side of the dilated triangle $T'S'=1.6$ cm, then the corresponding side of the original triangle $TS$ is $TS = 1.6\div\frac{1}{4}=1.6\times4 = 6.4$ cm.
If another side of the dilated triangle $S'R' = 2.1$ cm, then the corresponding side of the original triangle $SR$ is $SR=2.1\div\frac{1}{4}=2.1\times4 = 8.4$ cm.
If a side of the original triangle is $4$ cm, then the corresponding side of the dilated triangle is $4\times\frac{1}{4}=1$ cm.

Answer:

The side - length corresponding to the $1.6$ cm side in the dilated triangle in the original triangle is $6.4$ cm. The side - length corresponding to the $2.1$ cm side in the dilated triangle in the original triangle is $8.4$ cm. The side - length corresponding to the $4$ cm side in the original triangle in the dilated triangle is $1$ cm.