Question

directions: the pairs of polygons below are similar. give the scale factor of figure a to figure b.
2.
3.

1. if the scale factor of figure a to figure b is 4:5, find the value of x.
2. if the scale factor of figure a to figure b is 7:2, find the perimeter of figure a.

Explanation:

Step1: For 2

Find ratio of corresponding sides.
$\frac{2}{4}=\frac{1}{2}$

Step2: For 3

Find ratio of corresponding sides.
$\frac{10}{6}=\frac{5}{3}$

Step3: For 4

Set up proportion $\frac{4}{5}=\frac{x}{15}$.
Cross - multiply: $5x = 4\times15$.
Solve for $x$: $x=\frac{4\times15}{5}=12$

Step4: For 5

First find perimeter of Figure B: $12 + 9+9 + 5=35$.
Let perimeter of Figure A be $P_A$.
Set up proportion $\frac{7}{2}=\frac{P_A}{35}$.
Cross - multiply: $2P_A=7\times35$.
Solve for $P_A$: $P_A=\frac{7\times35}{2}=\frac{147}{2}$

Answer:

1. $\frac{1}{2}$
2. $\frac{5}{3}$
3. $12$
4. $\frac{147}{2}$