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Right Triangle Pythagorean Worksheet

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Right Triangle Pythagorean Worksheet worksheet preview

Right Triangle Pythagorean Worksheet

Right triangle illustration

📐 Part 1: Achieved Level - Finding the Hypotenuse

1. Calculate the hypotenuse of a right triangle with legs of 3 cm and 4 cm.

Hypotenuse = _______ cm

2. A right triangle has legs measuring 5 metres and 12 metres. What is the length of the hypotenuse?

Hypotenuse = _______ metres

3. Which of the following is a Pythagorean triad?

3, 4, 5

2, 3, 4

1, 2, 3

4, 5, 6

4. A ladder leans against a wall. The bottom of the ladder is 6 metres from the wall, and the ladder reaches 8 metres up the wall. How long is the ladder?

Ladder length = _______ metres

📊 Part 2: Merit Level - Finding Missing Sides

5. In a right triangle, the hypotenuse is 13 cm and one leg is 5 cm. Find the length of the other leg.

Missing leg = _______ cm

6. A rectangular field is 40 metres long and 30 metres wide. What is the diagonal distance across the field?

Diagonal distance = _______ metres

7. The hypotenuse of a right triangle is 25 metres and one leg is 20 metres. Calculate the area of the triangle.

Area = _______ square metres

8. A television screen measures 32 cm diagonally. If the width is 28 cm, what is the height?

Height = _______ cm

🏆 Part 3: Excellence Level - Complex Applications

9. A square has a diagonal of 10√2 cm. What is the perimeter of the square?

Perimeter = _______ cm

10. Two ships leave a harbour at the same time. Ship A travels 15 kilometres north, and Ship B travels 20 kilometres east. How far apart are the ships?

Distance apart = _______ kilometres

11. A right triangle has sides in the ratio 5:12:13. If the shortest side is 15 cm, find the area of the triangle.

Area = _______ square centimetres

12. Challenge: A rectangular prism has dimensions 6 cm × 8 cm × 10 cm. What is the length of the space diagonal (from one corner to the opposite corner)?

Space diagonal = _______ cm

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