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Pythagoras Mixed Problem Practice
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Pythagoras Mixed Problem Practice
📐 Part 1: Quick Recall
1. Write down Pythagoras' theorem formula:
2. In a right-angled triangle, which side is the hypotenuse?
The shortest side
The side opposite the right angle
Any of the three sides
The side adjacent to the right angle
3. Calculate the missing side in this right-angled triangle: sides 3cm and 4cm are given.
🏠 Part 2: Real-Life Applications
4. A ladder is leaning against a wall. The ladder is 5 metres long and the bottom of the ladder is 3 metres from the wall. How high up the wall does the ladder reach?
5. A rectangular field measures 80 metres by 60 metres. What is the length of the diagonal path across the field?
6. On a coordinate grid, point A is at (2, 3) and point B is at (6, 6). Calculate the distance between points A and B.
📊 Part 3: Composite Shapes
7. An isosceles triangle has a base of 12cm and equal sides of 10cm each. Find the height of the triangle.
8. A square has sides of 8cm. What is the length of its diagonal?
9. In an isosceles trapezium, the parallel sides are 16cm and 8cm apart. The slanted sides are each 10cm long. Find the height of the trapezium.
🎯 Part 4: Problem Solving
10. A television screen measures 32 inches diagonally. If the width is 28 inches, what is the height? (Round to 1 decimal place)
11. Two ships leave a port at the same time. Ship A travels 15 miles north, and Ship B travels 20 miles east. How far apart are the two ships?
12. Which of these situations would require Pythagoras' theorem? (Tick all that apply)
Finding the area of a rectangle
Calculating the diagonal of a square
Finding the distance between two points on a map
Working out the perimeter of a triangle
Calculating how high a ladder reaches on a wall
🧠 Part 5: Reasoning and Extension
13. Explain in your own words when and why you would use Pythagoras' theorem:
14. A right-angled triangle has sides in the ratio 3:4:5. If the shortest side is 9cm, what are the lengths of the other two sides?
15. Challenge: Draw a diagram to show how Pythagoras' theorem works with a square built on each side of a right-angled triangle:
✅ Part 6: Self-Assessment
16. Rate your confidence with each skill (1 = not confident, 5 = very confident):
Identifying when to use Pythagoras' theorem: _____ / 5
Setting up the equation correctly: _____ / 5
Solving real-life problems using the theorem: _____ / 5
Working with composite shapes: _____ / 5
17. What is one thing you found challenging about today's work?
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