Scale Factor practice 7th 10 16 2020 online exercise for | Live ... - Free Printable

To solve the problem of finding the missing side lengths in similar polygons, we need to use the concept of similarity ratios (scale factors). When two polygons are similar, their corresponding sides are proportional. This means that the ratio of the lengths of corresponding sides is constant.

Let's solve each part step by step:

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Problem 1:

The given trapezoids are similar. The side lengths are:
- Left trapezoid: 14 and 5
- Right trapezoid: ? and 25

#### Step 1: Identify the corresponding sides.
The side labeled "14" on the left corresponds to the unknown side "?" on the right.
The side labeled "5" on the left corresponds to the side labeled "25" on the right.

#### Step 2: Set up the proportion using the scale factor.
The scale factor can be determined from the known sides:
\[
\text{Scale factor} = \frac{\text{Right side}}{\text{Left side}} = \frac{25}{5} = 5
\]

#### Step 3: Use the scale factor to find the missing side.
The missing side "?" corresponds to the side "14" on the left:
\[
? = 14 \times 5 = 70
\]

#### Final Answer for Problem 1:
\[
\boxed{70}
\]

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Problem 2:

The given trapezoids are similar. The side lengths are:
- Left trapezoid: 10 and ?
- Right trapezoid: 15 and 24

#### Step 1: Identify the corresponding sides.
The side labeled "10" on the left corresponds to the side labeled "15" on the right.
The side labeled "?" on the left corresponds to the side labeled "24" on the right.

#### Step 2: Set up the proportion using the scale factor.
The scale factor can be determined from the known sides:
\[
\text{Scale factor} = \frac{\text{Right side}}{\text{Left side}} = \frac{15}{10} = 1.5
\]

#### Step 3: Use the scale factor to find the missing side.
The missing side "?" corresponds to the side "24" on the right:
\[
? = \frac{24}{1.5} = 16
\]

#### Final Answer for Problem 2:
\[
\boxed{16}
\]

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Problem 3:

The given rectangles are similar. The side lengths are:
- Left rectangle: 15 (all sides equal)
- Right rectangle: ? (all sides equal)

#### Step 1: Identify the corresponding sides.
All sides of the left rectangle are 15.
All sides of the right rectangle are ?.

#### Step 2: Use the given scale factor.
The problem states the scale factor is \(1:3\). This means:
\[
\text{Scale factor} = 3
\]

#### Step 3: Use the scale factor to find the missing side.
The missing side "?" corresponds to the side "15" on the left:
\[
? = 15 \times 3 = 45
\]

#### Final Answer for Problem 3:
\[
\boxed{45}
\]

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Problem 4:

The given triangles are similar. The side lengths are:
- Left triangle: 15 and 21
- Right triangle: 25 and ?

#### Step 1: Identify the corresponding sides.
The side labeled "15" on the left corresponds to the side labeled "25" on the right.
The side labeled "21" on the left corresponds to the unknown side "?" on the right.

#### Step 2: Set up the proportion using the scale factor.
The scale factor can be determined from the known sides:
\[
\text{Scale factor} = \frac{\text{Right side}}{\text{Left side}} = \frac{25}{15} = \frac{5}{3}
\]

#### Step 3: Use the scale factor to find the missing side.
The missing side "?" corresponds to the side "21" on the left:
\[
? = 21 \times \frac{5}{3} = 35
\]

#### Final Answer for Problem 4:
\[
\boxed{35}
\]

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Final Answers:

1. \(\boxed{70}\)
2. \(\boxed{16}\)
3. \(\boxed{45}\)
4. \(\boxed{35}\)