Question

using similar polygons
the polygons in each pair are similar. find the missing side length.
1)
two rectangles, first with width 10 and unknown height, second with width 15 and height 24
2)
two trapezoids, first with top base 12, bottom base 24, unknown leg, second with top base 15, leg 25
3)
two triangles, first with sides 10, 8, 14, second with side 4, base 7, unknown side
4)
two parallelograms, first with base 6, side 5, second with base 12, unknown side
5)
two parallelograms, first with sides 12, 10, 12, second with side 6, unknown side
6)
two triangles, first with sides 48, 54, unknown base, second with hypotenuse 63, leg 35, base 56
7)
two rectangles, first with height 6, second with unknown height, scale factor from a to b = 2 : 7
8)
two parallelograms, first with side 12, second with unknown side, scale factor from a to b = 2 : 3
9)
two trapezoids, first with unknown leg, second with leg 30, scale factor from a to b = 5 : 6
10)
two triangles, first with unknown side, second with side 7, scale factor from a to b = 1 : 7
11)
two parallelograms, first with base 9, second with unknown base, scale factor from a to b = 2 : 3
12)
two trapezoids, first with unknown top base, second with top base 6, scale factor from a to b = 1 : 2

Explanation:

Step1: Set up similarity proportion

For similar polygons, corresponding sides are proportional.

1. Let missing side = $x$. Proportion: $\frac{10}{15}=\frac{x}{24}$

Solve: $x = 24\times\frac{10}{15}=16$

1. Let missing side = $x$. Proportion: $\frac{12}{15}=\frac{x}{25}$

Solve: $x = 25\times\frac{12}{15}=20$

1. Let missing side = $x$. Proportion: $\frac{10}{x}=\frac{14}{7}$

Solve: $x = 10\times\frac{7}{14}=5$

1. Let missing side = $x$. Proportion: $\frac{6}{12}=\frac{5}{x}$

Solve: $x = 5\times\frac{12}{6}=10$

1. Let missing side = $x$. Proportion: $\frac{12}{6}=\frac{10}{x}$

Solve: $x = 10\times\frac{6}{12}=5$

1. Let missing side = $x$. Proportion: $\frac{x}{63}=\frac{48}{56}$

Solve: $x = 63\times\frac{48}{56}=54$

1. Let missing side = $x$. Use scale factor $\frac{2}{7}=\frac{6}{x}$

Solve: $x = 6\times\frac{7}{2}=21$

1. Let missing side = $x$. Use scale factor $\frac{2}{3}=\frac{12}{x}$

Solve: $x = 12\times\frac{3}{2}=18$

1. Let missing side = $x$. Use scale factor $\frac{5}{6}=\frac{x}{30}$

Solve: $x = 30\times\frac{5}{6}=25$

1. Let missing side = $x$. Use scale factor $\frac{1}{7}=\frac{x}{7}$

Solve: $x = 7\times\frac{1}{7}=1$

1. Let missing side = $x$. Use scale factor $\frac{2}{3}=\frac{9}{x}$

Solve: $x = 9\times\frac{3}{2}=13.5$

1. Let missing side = $x$. Use scale factor $\frac{1}{2}=\frac{x}{6}$

Solve: $x = 6\times\frac{1}{2}=3$

Answer:

1. 16
2. 20
3. 5
4. 10
5. 5
6. 54
7. 21
8. 18
9. 25
10. 1
11. 13.5
12. 3