Question

using similar polygons
the polygons in each pair are similar. find the missing side length.
1)
2)
3)
4)
5)
6)
7)
scale factor from a to b = 2 : 7
8)
scale factor from a to b = 2 : 3
9)
scale factor from a to b = 5 : 6
10)
scale factor from a to b = 1 : 7
11)
scale factor from a to b = 2 : 3
12)
scale factor from a to b = 1 : 2

Explanation:

Step1: Set up similarity proportion

$\frac{10}{15}=\frac{x}{24}$

Step2: Cross-multiply to solve for $x$

$15x=10\times24$
$15x=240$
$x=\frac{240}{15}=16$

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Step1: Set up similarity proportion

$\frac{12}{15}=\frac{24}{x}$

Step2: Cross-multiply to solve for $x$

$12x=15\times24$
$12x=360$
$x=\frac{360}{12}=30$

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Step1: Find similarity scale factor

$\frac{8}{4}=2$

Step2: Calculate missing side

$x=\frac{10}{2}=5$

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Step1: Find similarity scale factor

$\frac{6}{12}=\frac{1}{2}$

Step2: Calculate missing side

$x=5\div\frac{1}{2}=10$

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Step1: Find similarity scale factor

$\frac{12}{6}=2$

Step2: Calculate missing side

$x=\frac{10}{2}=5$

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Step1: Find similarity scale factor

$\frac{56}{48}=\frac{7}{6}$

Step2: Calculate missing side

$x=63\div\frac{7}{6}=63\times\frac{6}{7}=54$

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Step1: Set up scale factor proportion

$\frac{2}{7}=\frac{6}{x}$

Step2: Cross-multiply to solve for $x$

$2x=6\times7$
$2x=42$
$x=\frac{42}{2}=21$

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Step1: Set up scale factor proportion

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

Step2: Cross-multiply to solve for $x$

$3x=2\times12$
$3x=24$
$x=\frac{24}{3}=8$

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Step1: Set up scale factor proportion

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

Step2: Cross-multiply to solve for $x$

$6x=5\times30$
$6x=150$
$x=\frac{150}{6}=25$

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Step1: Set up scale factor proportion

$\frac{1}{7}=\frac{7}{x}$

Step2: Cross-multiply to solve for $x$

$1\times x=7\times7$
$x=49$

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Step1: Set up scale factor proportion

$\frac{2}{3}=\frac{x}{9}$

Step2: Cross-multiply to solve for $x$

$3x=2\times9$
$3x=18$
$x=\frac{18}{3}=6$

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Step1: Set up scale factor proportion

$\frac{1}{2}=\frac{x}{6}$

Step2: Cross-multiply to solve for $x$

$2x=1\times6$
$2x=6$
$x=\frac{6}{2}=3$

Answer:

1. 16
2. 30
3. 5
4. 10
5. 5
6. 54
7. 21
8. 8
9. 25
10. 49
11. 6
12. 3