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

Let’s solve each problem step by step. We’ll go one row at a time.

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Problem 14:

Actual triangle has sides: 3, 4, and hypotenuse (we can calculate it if needed, but maybe not necessary).
Scaled triangle has one side labeled 6 — which corresponds to the side of length 3 in the actual triangle.

→ So, scale factor = scaled side / actual side = 6 ÷ 3 = 2

Now, missing side in scaled triangle:
The side that was 4 in actual → scaled version is 4 × 2 = 8

✔ Scale Factor: 2
✔ Missing Side: 8

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Problem 15:

Actual triangle: base = 9, height = ? (but we don’t need it directly)
Scaled triangle: base = 12, height = 8

We can find scale factor using corresponding sides.

Assume the base scales from 9 to 12 → scale factor = 12 ÷ 9 = 4/3 ≈ 1.333...

Check with height: if actual height was h, then scaled height = h × (4/3) = 8 → so h = 8 × 3/4 = 6

So actual triangle had height 6, scaled has height 8 → matches.

Missing side in actual triangle: the hypotenuse? Wait — looking at diagram, probably the missing side is the height in actual triangle? But wait — in the scaled triangle, both base and height are given. In actual, only base is given (9), and one leg is missing.

Wait — actually, looking again: in actual triangle, two legs are shown: one is 9 (base), other is unknown. In scaled triangle, base is 12, height is 8.

Since they’re similar triangles, ratios must match.

So ratio of bases: 12 / 9 = 4/3 → scale factor from actual to scaled is 4/3.

Therefore, the missing side in actual triangle (the height) should be: scaled height divided by scale factor → 8 ÷ (4/3) = 8 × 3/4 = 6

But wait — the question says “What is the missing side?” — in the actual triangle, the vertical side is missing. So yes, it’s 6.

Alternatively, you could say: since scaled triangle’s height is 8, and scale factor is 4/3, then actual height = 8 × 3/4 = 6.

✔ Scale Factor: 4/3 (or 1.333...)
✔ Missing Side: 6

*(Note: Sometimes scale factor is written as a fraction. Let’s keep it as 4/3 for accuracy.)*

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Problem 16:

Actual rectangle: 20 by 20 → so it’s a square! Area = 20×20 = 400
Scaled rectangle: 30 by 30 → also a square! Area = 30×30 = 900

Scale factor: compare corresponding sides → 30 ÷ 20 = 3/2 = 1.5

Missing side in scaled rectangle? Both sides are given as 30 — so maybe the diagram shows one side labeled 30 and the other blank? But according to text, it says “30” on top and “30” on side — so perhaps no missing side? Wait — let me re-read.

Actually, looking back: “Actual: 20 x 20”, “Scale: 30 x ___” — oh! Probably the scaled rectangle has one side 30, and the other side is missing? But that wouldn’t make sense because if it’s scaled uniformly, both sides should scale same.

Wait — maybe the diagram shows actual rectangle 20x20, scaled rectangle has width 30, and height missing? But since it's a rectangle scaled proportionally, height should also be 30.

Unless... is it possible that only one dimension is scaled? No — scale factor applies to all dimensions.

Perhaps the “missing side” refers to something else? Or maybe it’s a trick?

Wait — let’s read carefully: “What is the missing side?” — in the scaled rectangle, if one side is 30, and actual was 20, then scale factor is 30/20 = 1.5, so the other side (which was 20) becomes 20 × 1.5 = 30. So missing side is 30.

But that seems too obvious. Maybe the diagram shows different labeling? Since I can’t see the image, I have to go by text.

Text says: Actual: 20 x 20; Scale: 30 x ___. So likely, the second dimension in scaled is missing → answer is 30.

Perimeter of actual rectangle: 2*(20+20) = 80
Perimeter of scaled rectangle: 2*(30+30) = 120

Area of actual: 400
Area of scaled: 900

✔ Scale Factor: 1.5 or 3/2
✔ Missing Side: 30
✔ Perimeter Actual: 80
✔ Perimeter Scaled: 120
✔ Area Actual: 400
✔ Area Scaled: 900

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Problem 17:

Actual rectangle: smaller one, area = 12 cm²
Scaled rectangle: larger one, one side is 6 cm (probably the width), and we’re told the actual rectangle was enlarged by scale factor of 2:1 → meaning scale factor = 2

So, every side in scaled is 2 times the actual.

First, what are the dimensions of actual rectangle?

We know area = 12 cm². But we don’t know length and width. However, in the diagram, probably the actual rectangle has width labeled? Wait — text says: “Actual: [small rectangle]”, “Scale: [large rectangle with width 6]”

And note: “The actual rectangle has been enlarged by a scale factor of 2:1”

So scale factor = 2

That means: scaled width = 2 × actual width

Given scaled width = 6 cm → so actual width = 6 ÷ 2 = 3 cm

Then, since area of actual = 12 cm², and width = 3 cm, then length = area ÷ width = 12 ÷ 3 = 4 cm

So actual rectangle is 3 cm by 4 cm

Then scaled rectangle: width = 6 cm, length = 4 × 2 = 8 cm

Now, questions:

- What is the missing side of the SCALE rectangle? → probably the length, which is 8 cm

- What is the perimeter of the ACTUAL rectangle? → 2*(3+4) = 14 cm

- What is the perimeter of the SCALE rectangle? → 2*(6+8) = 28 cm

- What is the area of the SCALE rectangle? → 6*8 = 48 cm²

(Also, check: area scale factor is square of linear scale factor → 2²=4, so 12*4=48 — correct!)

✔ Missing Side (scaled): 8 cm
✔ Perimeter Actual: 14 cm
✔ Perimeter Scaled: 28 cm
✔ Area Scaled: 48 cm²

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Now, compiling all answers:

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Final Answer:

Problem 14:
Scale Factor: 2
Missing Side: 8

Problem 15:
Scale Factor: 4/3
Missing Side: 6

Problem 16:
Scale Factor: 3/2
Missing Side: 30
Perimeter of Actual Rectangle: 80
Perimeter of Scaled Rectangle: 120
Area of Actual Rectangle: 400
Area of Scaled Rectangle: 900

Problem 17:
Missing Side of Scaled Rectangle: 8 cm
Perimeter of Actual Rectangle: 14 cm
Perimeter of Scaled Rectangle: 28 cm
Area of Scaled Rectangle: 48 cm²