Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. these two triangular prisms are similar. figure 2 is similar to figure 1 by a scale factor of 4. if the perimeter of abc is 21 cm, the perimeter of pqr is cm

Explanation:

Step1: Recall the property of similar - figures

For similar figures, the ratio of their perimeters is equal to the scale - factor.
Let the perimeter of $\triangle ABC$ be $P_1 = 21$ cm and the perimeter of $\triangle PQR$ be $P_2$. The scale - factor $k = 4$.
We know that $\frac{P_2}{P_1}=k$.

Step2: Calculate the perimeter of $\triangle PQR$

Substitute $P_1 = 21$ cm and $k = 4$ into the formula $\frac{P_2}{P_1}=k$. Then $P_2=k\times P_1$.
$P_2 = 4\times21=84$ cm.

Answer:

84