Question

13)
scale factor from a to b = 6 : 7
14)
scale factor from a to b = 1 : 3
solve for x. the polygons in each pair are similar.
15)
16)
17)
18)
19)
scale factor from a to b = 5 : 6
20)
scale factor from a to b = 5 : 6
21)
scale factor from a to b = 2 : 7
22)
scale factor from a to b = 6 : 7

Explanation:

13) Step1: Set up proportion

$\frac{x}{35} = \frac{6}{7}$

13) Step2: Solve for x

$x = 35 \times \frac{6}{7} = 30$

14) Step1: Set up proportion

$\frac{x}{27} = \frac{1}{3}$

14) Step2: Solve for x

$x = 27 \times \frac{1}{3} = 9$

15) Step1: Find similarity ratio

$\frac{42}{49} = \frac{6}{7}$

15) Step2: Set up proportion

$\frac{8x-2}{63} = \frac{6}{7}$

15) Step3: Isolate term with x

$8x-2 = 63 \times \frac{6}{7} = 54$

15) Step4: Solve for x

$8x = 56 \implies x = 7$

16) Step1: Find similarity ratio

$\frac{18}{24} = \frac{3}{4}$

16) Step2: Set up proportion

$\frac{x-2}{12} = \frac{3}{4}$

16) Step3: Isolate term with x

$x-2 = 12 \times \frac{3}{4} = 9$

16) Step4: Solve for x

$x = 11$

17) Step1: Find similarity ratio

$\frac{35}{30} = \frac{7}{6}$

17) Step2: Set up proportion

$\frac{63}{6x-6} = \frac{7}{6}$

17) Step3: Cross multiply

$7(6x-6) = 63 \times 6$

17) Step4: Simplify and solve

$6x-6 = 54 \implies 6x=60 \implies x=10$

18) Step1: Find similarity ratio

$\frac{16}{40} = \frac{2}{5}$

18) Step2: Set up proportion

$\frac{2x+4}{45} = \frac{2}{5}$

18) Step3: Isolate term with x

$2x+4 = 45 \times \frac{2}{5} = 18$

18) Step4: Solve for x

$2x=14 \implies x=7$

19) Step1: Set up proportion

$\frac{3x+11}{42} = \frac{5}{6}$

19) Step2: Isolate term with x

$3x+11 = 42 \times \frac{5}{6} = 35$

19) Step3: Solve for x

$3x=24 \implies x=8$

20) Step1: Set up proportion

$\frac{30}{3x} = \frac{5}{6}$

20) Step2: Cross multiply

$15x = 180$

20) Step3: Solve for x

$x=12$

21) Step1: Set up proportion

$\frac{14}{8x-7} = \frac{2}{7}$

21) Step2: Cross multiply

$2(8x-7) = 14 \times 7$

21) Step3: Simplify and solve

$8x-7 = 49 \implies 8x=56 \implies x=7$

22) Step1: Set up proportion

$\frac{48}{8x} = \frac{6}{7}$

22) Step2: Cross multiply

$48x = 48 \times 7$

22) Step3: Solve for x

$x=7$

Answer:

1. $x=30$
2. $x=9$
3. $x=7$
4. $x=11$
5. $x=10$
6. $x=7$
7. $x=8$
8. $x=12$
9. $x=7$
10. $x=7$