Let's solve each problem step by step to find the
scale factor between the two similar shapes. The
scale factor is the ratio of the lengths of corresponding sides in two similar figures.
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Problem 1:
We have two triangles:
-
Small triangle: sides = 10, 10, 5
-
Large triangle: sides = 50, 50, 25
We compare corresponding sides:
- 10 → 50 → ratio = 10/50 = 1/5
- 10 → 50 → ratio = 10/50 = 1/5
- 5 → 25 → ratio = 5/25 = 1/5
All ratios are
1:5, so the
scale factor from the small triangle to the large triangle is
1:5.
✔ Answer: C) 1:5
> Note: Scale factor is usually written as
small : large unless otherwise specified. Here, since the second triangle is larger, the scale factor from the first to the second is
1:5.
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Problem 2:
Two quadrilaterals with side lengths:
-
First shape: 8, 28, 30, 18
-
Second shape: 12, 42, 45, 27
Let’s check the ratios of corresponding sides:
- 8 → 12 → 8/12 = 2/3
- 28 → 42 → 28/42 = 2/3
- 30 → 45 → 30/45 = 2/3
- 18 → 27 → 18/27 = 2/3
All ratios are
2:3, so the scale factor from the first shape to the second is
2:3.
✔ Answer: B) 2:3
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✔ Final Answers:
1.
C) 1:5
2.
B) 2:3
Let me know if you'd like a visual explanation or how to simplify ratios!
Parent Tip: Review the logic above to help your child master the concept of scale factors worksheet.
