Calculating Scale Factor Worksheet Practice by Middle School Math ... - Free Printable

It looks like you've uploaded a worksheet titled "Scale Factor Checkpoint" that contains several problems involving scale factors, actual measurements, and scaled drawings. Since I can't view images directly, I'll help you solve the problems based on the text you provided.

Let me go through each problem step by step and explain how to solve them.

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Problem 48:

Actual: A triangle with sides labeled as:
- One side = 10 cm
- Another side = 15 cm
- Third side = 20 cm

Scale: 1:2
(That means every dimension in the drawing is half of the actual size.)

#### Questions:
a) What is the scale factor?
b) What is the actual perimeter?

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#### Solution:

a) Scale Factor:
The scale is given as 1:2, which means:
> The drawing is 1 unit for every 2 units in real life.

So, scale factor from actual to drawing is $ \frac{1}{2} $.
But if we're going from drawing to actual, it's $ 2 $.

Typically, scale factor refers to the ratio of drawing to actual, so:

> Scale factor = 1/2

✔ Answer: 1/2

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b) Actual Perimeter:
We are given the actual triangle has sides: 10 cm, 15 cm, 20 cm.

So, perimeter = $ 10 + 15 + 20 = 45 $ cm

✔ Answer: 45 cm

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Problem 49:

Actual: A right triangle with:
- Base = 12 cm
- Height = 9 cm
- Hypotenuse = ? (not needed)

Scale: 1:3

#### Questions:
a) What is the scale factor?
b) What is the actual perimeter?

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#### Solution:

a) Scale Factor:
Scale is 1:3 → Drawing : Actual = 1:3
So, scale factor = 1/3

✔ Answer: 1/3

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b) Actual Perimeter:
We have:
- Base = 12 cm
- Height = 9 cm
- Need hypotenuse → use Pythagorean theorem:

$$
\text{Hypotenuse} = \sqrt{12^2 + 9^2} = \sqrt{144 + 81} = \sqrt{225} = 15 \text{ cm}
$$

Perimeter = $ 12 + 9 + 15 = 36 $ cm

✔ Answer: 36 cm

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Problem 50:

Actual: A rectangle with:
- Length = 20 cm
- Width = 10 cm

Scale: 1:4

#### Questions:
a) What is the scale factor?
b) What is the perimeter of the SCALE rectangle?
c) What is the area of the SCALE rectangle?

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#### Solution:

a) Scale Factor:
Scale = 1:4 → Drawing is 1/4 of actual

✔ Scale factor = 1/4

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b) Perimeter of SCALE rectangle:

First, find scaled dimensions:
- Scaled length = $ 20 \times \frac{1}{4} = 5 $ cm
- Scaled width = $ 10 \times \frac{1}{4} = 2.5 $ cm

Perimeter = $ 2 \times (5 + 2.5) = 2 \times 7.5 = 15 $ cm

✔ Answer: 15 cm

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c) Area of SCALE rectangle:

Area = length × width = $ 5 \times 2.5 = 12.5 $ cm²

✔ Answer: 12.5 cm²

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Problem 51:

Actual: A small rectangle with height = 10 cm, width = ?
But the scaled rectangle is shown with:
- Height = 20 cm
- Width = 40 cm

And it says: *"This actual rectangle has been enlarged by a scale factor of 2.5"*

Wait — this seems reversed. Let’s read carefully.

> "The actual rectangle has been enlarged by a scale factor of 2.5"

So:
- Actual → Scaled using a scale factor of 2.5
- So, scaled = actual × 2.5

We are told the scaled rectangle has:
- Height = 20 cm
- Width = 40 cm

So, we need to find the actual dimensions.

#### Questions:
a) What is the scale factor?
b) What is the perimeter of the SCALE rectangle?
c) What is the area of the SCALE rectangle?

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#### Solution:

a) Scale Factor:
Given: Enlarged by a scale factor of 2.5

So, scale factor = 2.5

✔ Answer: 2.5

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b) Perimeter of SCALE rectangle:

Scaled rectangle:
- Height = 20 cm
- Width = 40 cm

Perimeter = $ 2 \times (20 + 40) = 2 \times 60 = 120 $ cm

✔ Answer: 120 cm

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c) Area of SCALE rectangle:

Area = $ 20 \times 40 = 800 $ cm²

✔ Answer: 800 cm²

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✔ Final Answers Summary:

| Problem | a) Scale Factor | b) Perimeter (Actual or Scale?) | c) Area (if applicable) |
|--------|------------------|-------------------------------|--------------------------|
| 48 | 1/2 | 45 cm | N/A |
| 49 | 1/3 | 36 cm | N/A |
| 50 | 1/4 | 15 cm | 12.5 cm² |
| 51 | 2.5 | 120 cm | 800 cm² |

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🔍 Key Concepts:

- Scale Factor: Ratio of drawing to actual.
- If scale is 1:2, then scale factor = 1/2
- If enlarged by 2.5, scale factor = 2.5
- Perimeter scales linearly with scale factor.
- Area scales with the square of the scale factor.
- E.g., if scale factor is 2.5, area increases by $ 2.5^2 = 6.25 $

Let me know if you'd like a version of this with all answers filled in the table format!