We are told that
parallelogram I is a scaled copy of parallelogram H, and we are to find the
scale factor that takes parallelogram $ H $ to parallelogram $ I $.
---
Step 1: Understand what a scale factor means
A
scale factor is the ratio of corresponding lengths in two similar figures. Since the shapes are scaled copies, their corresponding sides are proportional.
We can compute the scale factor by comparing corresponding side lengths from $ H $ to $ I $.
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Step 2: Identify corresponding sides
From the diagram:
- Parallelogram $ H $ has:
- One side = 35
- Adjacent side = 15
- Parallelogram $ I $ has:
- Corresponding side = 28
- Corresponding side = 12
We assume the sides are paired as follows:
- 35 in $ H $ corresponds to 28 in $ I $
- 15 in $ H $ corresponds to 12 in $ I $
Let’s check if both ratios give the same scale factor.
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Step 3: Compute the scale factor
#### Ratio of longer sides:
$$
\frac{28}{35} = \frac{4}{5} = 0.8
$$
#### Ratio of shorter sides:
$$
\frac{12}{15} = \frac{4}{5} = 0.8
$$
Both ratios are equal! So the scale factor is consistent.
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✔ Final Answer:
$$
\boxed{\frac{4}{5}}
$$
This means that
parallelogram I is a scaled-down version of parallelogram H by a scale factor of $ \frac{4}{5} $.
Parent Tip: Review the logic above to help your child master the concept of scale factor word problems worksheet.
