Bridge Design Geometry Challenge

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Date:

🔧 Part 1: Geometric Calculations

1. A triangular bridge support has sides of 8 cm and 6 cm. Use Pythagoras' theorem to calculate the length of the hypotenuse.

2. Your bridge design uses congruent triangular supports. If one triangle has angles of 45°, 45°, and 90°, what type of triangle is this?

Scalene triangle

Isosceles right triangle

Equilateral triangle

Obtuse triangle

3. A bridge deck is 50 cm long and needs diagonal supports every 10 cm. How many diagonal supports are needed?

Answer: _________ diagonal supports

4. Calculate the area of a rectangular bridge platform that is 25 cm long and 8 cm wide.

5. Two bridge supports form similar triangles. If the first triangle has sides of 6 cm, 8 cm, and 10 cm, and the second triangle's shortest side is 9 cm, what are the lengths of the other two sides?

🏗️ Part 2: Bridge Design Analysis

6. Explain why triangular supports are commonly used in bridge construction. Include at least two geometric reasons.

7. Which factors affect load distribution in a bridge? Tick all that apply:

Shape of supports

Angle of supports

Material strength

Colour of the bridge

Distance between supports

8. A bridge support makes a 60° angle with the horizontal deck. If the vertical height is 12 cm, calculate the length of the support beam using trigonometry.

9. Describe how you would test whether two triangular supports in your bridge design are congruent.

💭 Part 3: Design Reflection

10. Sketch your bridge design in the space below. Label at least three geometric features (angles, lengths, or shapes).

11. What mathematical strategies did you use to ensure your bridge design would be stable? Explain your reasoning.

12. If you could redesign your bridge, what geometric changes would you make to improve its load-bearing capacity? Justify your answer using mathematical concepts.