Worksheet for Grade 7 students to practice calculating the missing side lengths of geometric shapes using given perimeters.

Here is the step-by-step solution for each problem, using the definition of perimeter — the total length around a shape.

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Problem 1: Rectangle

- Given: One side = 6 cm, adjacent side = x cm, Perimeter = 30 cm
- A rectangle has 2 pairs of equal sides → perimeter = 2 × (length + width)
- Equation:
`2(6 + x) = 30`
→ `6 + x = 15`
→ `x = 9`

✔ Answer: x = 9 cm

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Problem 2: Rectangle

- Given: One side = x cm, adjacent side = 12 cm, Perimeter = 90 cm
- Equation:
`2(x + 12) = 90`
→ `x + 12 = 45`
→ `x = 33`

✔ Answer: x = 33 cm

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Problem 3: Square

- All sides equal → labeled as x
- Perimeter = 4 × side → `4x = 40`
→ `x = 10`

✔ Answer: x = 10 cm

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Problem 4: Isosceles Triangle

- Two sides are equal (marked with “x”), base = 18 cm, Perimeter = 25 cm
- So: `x + x + 18 = 25`
→ `2x = 7`
→ `x = 3.5`

✔ Answer: x = 3.5 cm

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Problem 5: Equilateral Triangle

- All three sides equal → all labeled x
- Perimeter = 3x = 21
→ `x = 7`

✔ Answer: x = 7 cm

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Problem 6: Isosceles Triangle

- Two sides = x, base = 20 cm, Perimeter = 64 cm
- Equation: `x + x + 20 = 64`
→ `2x = 44`
→ `x = 22`

✔ Answer: x = 22 cm

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Problem 7: Parallelogram

- Opposite sides equal → two sides = 5 cm, two sides = x cm
- Perimeter = 2×5 + 2×x = 60
→ `10 + 2x = 60`
→ `2x = 50`
→ `x = 25`

✔ Answer: x = 25 cm

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Problem 8: Regular Pentagon

- All 5 sides equal → each side = x
- Perimeter = 5x = 4
→ `x = 4/5 = 0.8`

✔ Answer: x = 0.8 cm

*(Note: This seems unusually small, but mathematically correct based on given perimeter.)*

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Problem 9: Composite Shape (House-like)

- The shape has:
- 2 vertical sides = 40 cm each
- 1 bottom side = 20 cm
- 2 slanted roof sides = x cm each
- Total perimeter = 40 + 40 + 20 + x + x = 140
→ `100 + 2x = 140`
→ `2x = 40`
→ `x = 20`

✔ Answer: x = 20 cm

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## ✔ Final Answers:

1. x = 9 cm
2. x = 33 cm
3. x = 10 cm
4. x = 3.5 cm
5. x = 7 cm
6. x = 22 cm
7. x = 25 cm
8. x = 0.8 cm
9. x = 20 cm

Let me know if you’d like diagrams or further explanations!