Question

kuta software - infinite geometry
name:
proportional parts in triangles and parallel lines
date_ period
find the missing length indicated.
1)
2)
3)
4)
solve for x.
5)
6)
find the missing length indicated.
7)
8)
-1-

Explanation:

Step1: Set up proportion for similar triangles

$\frac{?}{15} = \frac{14-4}{14}$

Step2: Simplify and solve for unknown

$\frac{?}{15} = \frac{10}{14} = \frac{5}{7}$
$? = 15 \times \frac{5}{7} = \frac{75}{7} \approx 10.71$

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Step1: Set up proportion for similar triangles

$\frac{?}{25} = \frac{24}{15}$

Step2: Solve for unknown

$? = 25 \times \frac{24}{15} = 40$

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Step1: Set up proportion for similar triangles

$\frac{?}{18} = \frac{20}{20+8}$

Step2: Simplify and solve for unknown

$\frac{?}{18} = \frac{20}{28} = \frac{5}{7}$
$? = 18 \times \frac{5}{7} = \frac{90}{7} \approx 12.86$

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Step1: Set up proportion for similar triangles

$\frac{?}{15} = \frac{2}{12-2}$

Step2: Simplify and solve for unknown

$\frac{?}{15} = \frac{2}{10} = \frac{1}{5}$
$? = 15 \times \frac{1}{5} = 3$

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Step1: Set up proportion for similar triangles

$\frac{5x}{45} = \frac{20}{36}$

Step2: Simplify and solve for x

$\frac{x}{9} = \frac{5}{9}$
$x = 5$

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Step1: Set up proportion for similar triangles

$\frac{3x-5}{10} = \frac{28-8}{28}$

Step2: Simplify and solve for x

$\frac{3x-5}{10} = \frac{20}{28} = \frac{5}{7}$
$3x-5 = \frac{50}{7}$
$3x = \frac{50}{7} + 5 = \frac{85}{7}$
$x = \frac{85}{21} \approx 4.05$

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Step1: Set up proportion for similar triangles

$\frac{?}{25} = \frac{6}{15}$

Step2: Solve for unknown

$? = 25 \times \frac{6}{15} = 10$

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Step1: Set up proportion for similar triangles

$\frac{?}{77} = \frac{30}{30+25}$

Step2: Simplify and solve for unknown

$\frac{?}{77} = \frac{30}{55} = \frac{6}{11}$
$? = 77 \times \frac{6}{11} = 42$

Answer:

1. $\boldsymbol{\frac{75}{7}}$
2. $\boldsymbol{40}$
3. $\boldsymbol{\frac{90}{7}}$
4. $\boldsymbol{3}$
5. $\boldsymbol{x=5}$
6. $\boldsymbol{x=\frac{85}{21}}$
7. $\boldsymbol{10}$
8. $\boldsymbol{42}$