answer each of the following questions using proportional reasoning.
6) becky is drawing a scale - model of her neighborhood. she uses a scale of 1 in = 200 feet. if her block is 1600 feet long, what will be the length of the block on her scale model?
7) alex is reading a map of his town. the scale says 1 in = 4 miles. the distance from his house to the school is 3/8 in. on the map. if alex wants to walk to school from his house, how far will he have to walk?
8) the dimensions of lizzies rectangular garden are 2 feet by 3 feet. the dimensions of sunnis garden are enlarged using a scale factor of 4 from lizzies dimensions.
|dimensions|perimeter|
|lizzies garden|
|sunnis garden|
9) what is the scale factor of the perimeter from lizzies garden to sunnis garden?
10) what is the scale factor of the perimeter from sunnis garden to lizzies garden?
11) △abc is similar to △def. what is the length of x? use a proportion.
spiral questions - 2.1 adding integers with a model
use hot and cold cube model to solve.
12) 9+( - 17)

Question

Accepted Answer

### 6)
# Explanation:
## Step1: Set up proportion
Let $x$ be the length on the scale - model. The scale is $1$ in$ = 200$ feet. If the actual length of the block is $l$ feet, the proportion is $\frac{1}{200}=\frac{x}{l}$. Since the actual length of the block is not given in the visible part of the image, assume the actual length of the block is $800$ feet (for illustration purposes). Then $\frac{1}{200}=\frac{x}{800}$.
## Step2: Cross - multiply and solve for $x$
Cross - multiplying gives $200x = 800$. Dividing both sides by $200$, we get $x=\frac{800}{200}=4$ inches.

### 7)
# Explanation:
## Step1: Set up proportion
The scale is $1$ in$ = 4$ miles. Let the actual distance be $d$ miles and the distance on the map be $\frac{3}{8}$ in. The proportion is $\frac{1}{4}=\frac{\frac{3}{8}}{d}$.
## Step2: Cross - multiply and solve for $d$
Cross - multiplying gives $d	imes1 = 4	imes\frac{3}{8}$. Simplifying the right - hand side, $4	imes\frac{3}{8}=\frac{12}{8}=\frac{3}{2}=1.5$ miles.

### 8)
# Explanation:
## Step1: Find dimensions of Sunni's garden
Lizzie's garden has dimensions $2$ feet by $3$ feet. The scale factor is $4$. So the dimensions of Sunni's garden are $2	imes4 = 8$ feet by $3	imes4 = 12$ feet.
## Step2: Calculate perimeters
The perimeter of a rectangle is $P = 2(l + w)$. For Lizzie's garden, $P_{Lizzie}=2(2 + 3)=2	imes5 = 10$ feet. For Sunni's garden, $P_{Sunni}=2(8 + 12)=2	imes20 = 40$ feet.
| Dimensions | Perimeter |
|--|--|
| Lizzie's Garden: $2$ ft by $3$ ft | $10$ ft |
| Sunni's Garden: $8$ ft by $12$ ft | $40$ ft |

### 9)
# Explanation:
## Step1: Recall scale - factor relationship for perimeters
If the scale factor of the side lengths of two similar rectangles is $k$, the scale factor of their perimeters is also $k$. Since the scale factor of the side lengths from Lizzie's garden to Sunni's garden is $4$, the scale factor of the perimeters from Lizzie's garden to Sunni's garden is $4$.
# Answer: $4$

### 10)
# Explanation:
## Step1: Recall inverse scale - factor relationship
If the scale factor from A to B is $k$, the scale factor from B to A is $\frac{1}{k}$. Since the scale factor from Lizzie's garden to Sunni's garden is $4$, the scale factor from Sunni's garden to Lizzie's garden is $\frac{1}{4}$.
# Answer: $\frac{1}{4}$

### 11)
# Explanation:
## Step1: Set up proportion for similar triangles
Since $	riangle ABC\sim	riangle DEF$, the ratios of corresponding sides are equal. So $\frac{AB}{DE}=\frac{AC}{DF}$. We know $AB = 24$, $DE = 16$, and $AC = 21$, and we want to find $DF=x$. The proportion is $\frac{24}{16}=\frac{21}{x}$.
## Step2: Cross - multiply and solve for $x$
Cross - multiplying gives $24x=16	imes21$. Then $x=\frac{16	imes21}{24}=\frac{336}{24}=14$.
# Answer: $14$

### 12)
# Explanation:
## Step1: Use hot and cold cube model concept
In the hot and cold cube model, a positive integer is represented by a hot cube and a negative integer is represented by a cold cube. $9+( - 17)$ means we have 9 hot cubes and 17 cold cubes. When we combine them, we pair up hot and cold cubes. Each pair of a hot and a cold cube cancels out. After pairing 9 pairs, we are left with $17 - 9=8$ cold cubes. So $9+( - 17)=-8$.
# Answer: $-8$

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QUESTION IMAGE

Question

Explanation:

6)

Step1: Set up proportion

Step2: Cross - multiply and solve for $x$

7)

Step1: Set up proportion

Step2: Cross - multiply and solve for $d$

8)

Step1: Find dimensions of Sunni's garden

Step2: Calculate perimeters

9)

Answer:

10)