Question

1. what is the scale factor of figure b to figure a?
2. given the similar figures below, find the value of x.
3. given figure abcd ~ figure ehgf, find ef.
4. given δjkl ~ δmnl, find jk.
5. a stop sign casts a shadow 8 feet long, while a school bus nearby casts a shadow 12 feet long. if the stop sign is 7 feet tall, how tall is the school bus?
6. a 54 - foot tall office building casts a shadow that is 48 feet long. if mindy is 56 tall and standing nearby, find the length of her shadow.

a. $3\frac{3}{4}$ feet c. $4\frac{1}{3}$ feet
b. $4\frac{1}{2}$ feet d. $4\frac{8}{9}$ feet
use the diagram below to answer questions 24 - 25.

1. which proportion could find x, the distance across griffin lake?

a. $\frac{64}{84}=\frac{x}{92}$ c. $\frac{64}{92}=\frac{84}{x}$
b. $\frac{x}{64}=\frac{84}{92}$ d. $\frac{84}{x}=\frac{92}{64}$

1. find x.

Explanation:

Step1: Define scale factor (B to A)

Scale factor = $\frac{\text{Side of A}}{\text{Side of B}}$

Step2: Calculate using matching sides

$\text{Scale factor} = \frac{20}{5} = 4$
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Step1: Set up proportion for similar triangles

$\frac{x}{10} = \frac{28}{23}$

Step2: Solve for $x$

$x = 10 \times \frac{28}{23} = \frac{280}{23} \approx 12.17$
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Step1: Find scale factor (ABCD to EHGF)

$\text{Scale factor} = \frac{10}{15} = \frac{2}{3}$

Step2: Calculate $EF$

$EF = 18 \times \frac{2}{3} = 12$
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Step1: Find scale factor (JKL to MNL)

$\text{Scale factor} = \frac{24}{20} = \frac{6}{5}$

Step2: Calculate $JK$

$JK = 12 \times \frac{6}{5} = 14.4$
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Step1: Set up height-shadow proportion

$\frac{\text{Bus height}}{12} = \frac{7}{8}$

Step2: Solve for bus height

$\text{Bus height} = 12 \times \frac{7}{8} = 10.5$
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Step1: Convert height to feet: $5'6'' = 5.5$ ft

Step2: Set up proportion

$\frac{5.5}{54} = \frac{\text{Shadow length}}{48}$

Step3: Solve for shadow length

$\text{Shadow length} = 5.5 \times \frac{48}{54} = \frac{44}{9} = 4\frac{8}{9}$
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Step1: Identify correct proportion for similar triangles

Corresponding sides: $\frac{64}{84} = \frac{x}{92}$
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Step1: Solve the proportion for $x$

$x = 92 \times \frac{64}{84} = \frac{92 \times 16}{21} = \frac{1472}{21} \approx 70.09$

Answer:

1. $4$
2. $x = \frac{280}{23}$ or $\approx 12.17$
3. $EF = 12$
4. $JK = 14.4$
5. $10.5$ feet
6. D. $4\frac{8}{9}$ feet
7. A. $\frac{64}{84} = \frac{x}{92}$
8. $x = \frac{1472}{21}$ or $\approx 70.09$ feet