Question

find the scale factor of each pair of similar triangles. 6) scale factor of p to q is ______ scale factor of q to p is ____ scale factor of k to l is ____ scale factor of l to k is ____ 7) scale factor of u to v is ____ scale factor of v to u is ____ 8) scale factor of c to d is ____ scale factor of d to c is ______

Explanation:

Step1: Recall scale - factor formula

The scale factor of two similar triangles from triangle $A$ to triangle $B$ is the ratio of the corresponding side lengths of $B$ to $A$.

Step2: For triangles $P$ and $Q$

Let's take the ratio of corresponding sides. For example, if we take the sides of length $8$ ft in $P$ and $24$ ft in $Q$. The scale factor of $P$ to $Q$ is $\frac{24}{8}=3$. The scale factor of $Q$ to $P$ is $\frac{8}{24}=\frac{1}{3}$.

Step3: For triangles $K$ and $L$

Taking the sides of length $16$ yd in $K$ and $9$ yd in $L$, the scale factor of $K$ to $L$ is $\frac{9}{16}$. The scale factor of $L$ to $K$ is $\frac{16}{9}$.

Step4: For triangles $U$ and $V$

Taking the sides of length $20$ in in $U$ and $8$ in in $V$, the scale factor of $U$ to $V$ is $\frac{8}{20}=\frac{2}{5}$. The scale factor of $V$ to $U$ is $\frac{20}{8}=\frac{5}{2}$.

Step5: For triangles $C$ and $D$

Taking the sides of length $5$ ft in $C$ and $20$ ft in $D$, the scale factor of $C$ to $D$ is $\frac{20}{5}=4$. The scale factor of $D$ to $C$ is $\frac{5}{20}=\frac{1}{4}$.

Answer:

Scale factor of $P$ to $Q$: $3$
Scale factor of $Q$ to $P$: $\frac{1}{3}$
Scale factor of $K$ to $L$: $\frac{9}{16}$
Scale factor of $L$ to $K$: $\frac{16}{9}$
Scale factor of $U$ to $V$: $\frac{2}{5}$
Scale factor of $V$ to $U$: $\frac{5}{2}$
Scale factor of $C$ to $D$: $4$
Scale factor of $D$ to $C$: $\frac{1}{4}$