Scale factor work sheet online exercise for - Free Printable

Let's solve each question step by step using the given figures.

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Given:

- Figure A is a right triangle with sides:
- Base = 12 in
- Height = 16 in
- Hypotenuse = 20 in

- Figure B is a right triangle with sides:
- Base = 3 in
- Height = 4 in
- Hypotenuse = 5 in

Both are right triangles, and their side lengths are proportional:
- 12 : 3 = 4
- 16 : 4 = 4
- 20 : 5 = 4

So, Figure A is a scaled-up version of Figure B by a factor of 4.

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1) What is the scale factor of figure A to figure B?

We compare corresponding sides:

$$
\frac{12}{3} = 4,\quad \frac{16}{4} = 4,\quad \frac{20}{5} = 4
$$

✔ So, the scale factor of A to B is 4:1.

> Answer: $ \boxed{4:1} $

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2) Determine the perimeters of figures A and B.

Perimeter of A = 12 + 16 + 20 = $ \boxed{48} $ inches

Perimeter of B = 3 + 4 + 5 = $ \boxed{12} $ inches

> Answer:
> - Perimeter of A: 48 in
> - Perimeter of B: 12 in

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3) What is the ratio of perimeters of figure A to figure B?

$$
\frac{\text{Perimeter of A}}{\text{Perimeter of B}} = \frac{48}{12} = 4
$$

So, the ratio is $ \boxed{4:1} $

> Answer: $ \boxed{4:1} $

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4) Find the areas of figure A and figure B.

Area of a right triangle = $ \frac{1}{2} \times \text{base} \times \text{height} $

Area of A = $ \frac{1}{2} \times 12 \times 16 = 6 \times 16 = \boxed{96} $ square inches

Area of B = $ \frac{1}{2} \times 3 \times 4 = 1.5 \times 4 = \boxed{6} $ square inches

> Answer:
> - Area of A: 96 in²
> - Area of B: 6 in²

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5) What is the ratio of areas of figure A to figure B?

$$
\frac{96}{6} = 16
$$

So, the ratio is $ \boxed{16:1} $

> Answer: $ \boxed{16:1} $

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6) Express the relationship between scale factor and the ratio of perimeters.

The ratio of perimeters is equal to the scale factor.

Since scale factor is 4:1, and perimeter ratio is also 4:1:

> ✔ The ratio of perimeters is equal to the scale factor.

> Answer: The ratio of perimeters is equal to the scale factor.

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7) What is the relation between scale factor and the ratio of areas?

Scale factor = 4:1
Ratio of areas = 16:1 = $ 4^2 : 1 $

So, the ratio of areas is the square of the scale factor.

> ✔ The ratio of areas is equal to the square of the scale factor.

> Answer: The ratio of areas is equal to the square of the scale factor.

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✔ Final Answers Summary:

1) Scale factor of A to B: 4:1
2) Perimeter of A: 48 in, Perimeter of B: 12 in
3) Ratio of perimeters: 4:1
4) Area of A: 96 in², Area of B: 6 in²
5) Ratio of areas: 16:1
6) The ratio of perimeters equals the scale factor.
7) The ratio of areas equals the square of the scale factor.

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This demonstrates a key geometric principle:

> 🔷 For similar figures:
> - Ratio of perimeters = scale factor
> - Ratio of areas = (scale factor)²

Let me know if you'd like this explained visually or with diagrams!