We are given 8 problems involving
similar polygons. Since the polygons are similar, their corresponding sides are proportional — meaning they have the same
scale factor.
Let’s solve each one step by step.
---
Problem 1:
Left polygon has side = 45
Right polygon has corresponding side = 60
Missing side on left corresponds to side = 8 on right.
Since the polygons are similar, set up a proportion:
>
Left / Right = 45 / 60 = ? / 8
Simplify 45/60 = 3/4
So:
>
? / 8 = 3/4
Multiply both sides by 8:
>
? = (3/4) × 8 = 6
✔ Answer: 6
---
Problem 2:
Scale Factor of Left to Right:
3 : 5
Right side = 75 → find corresponding left side.
Scale factor 3:5 means:
>
Left = (3/5) × Right
So:
>
Left = (3/5) × 75 = 45
✔ Answer: 45
---
Problem 3:
Scale Factor of Left to Right:
1 : 3
Right side = 30 → find corresponding left side.
>
Left = (1/3) × 30 = 10
✔ Answer: 10
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Problem 4:
Scale Factor of Left to Right:
5 : 6
Left side = 20 → find corresponding right side.
>
Right = (6/5) × Left = (6/5) × 20 = 24
✔ Answer: 24
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Problem 5:
Scale Factor of Left to Right:
1 : 4
Left side = 2 → find corresponding right side x.
>
x = 4 × 2 = 8
✔ Answer: 8
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Problem 6:
Scale Factor of Left to Right:
1 : 6
Left side = 3 → find corresponding right side x.
>
x = 6 × 3 = 18
✔ Answer: 18
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Problem 7:
Left square: sides 24 and 10
Right square: sides x and 36
Wait — if it's a
square, all sides must be equal. But here, left has sides 24 and 10? That’s a
rectangle, not a square. Probably a typo in labeling — we’ll treat it as a rectangle.
Assuming the sides correspond:
Left: 24 corresponds to x
Left: 10 corresponds to 36
Check scale factor from 10 → 36:
> Scale factor = 36 / 10 = 3.6
Then x = 24 × 3.6 =
86.4
Alternatively, if 24 corresponds to 36, then scale factor = 36/24 = 1.5 → then x = 10 × 1.5 = 15
But which pair corresponds?
Looking at the image layout:
- The
bottom side of left is 24 → bottom side of right is x
- The
right side of left is 10 → right side of right is 36
So we assume
vertical sides correspond to vertical sides,
horizontal to horizontal.
Thus:
> 10 → 36 ⇒ scale factor = 36/10 = 3.6
> So 24 → x = 24 × 3.6 =
86.4
✔ Answer: 86.4
*(Note: If the problem intended squares, then 24 should equal 10 — contradiction. So we go with rectangle interpretation.)*
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Problem 8:
Left trapezoid: sides x and 7
Right trapezoid: sides 24 and 14
Assume corresponding sides:
- Side 7 corresponds to 14
- Side x corresponds to 24
Check scale factor:
> 14 / 7 = 2 → so right is twice left.
Thus:
> x × 2 = 24 → x = 24 / 2 =
12
✔ Answer: 12
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##
✔ Final Answers:
1)
6
2)
45
3)
10
4)
24
5)
8
6)
18
7)
86.4
8)
12
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Let me know if you want these boxed or formatted for submission!
Parent Tip: Review the logic above to help your child master the concept of similar shapes proportions worksheet.
