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Right Triangle Pythagorean Worksheet
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Right Triangle Pythagorean Worksheet
A pizza shop is planning deliveries and checking its equipment. Use the Pythagorean theorem, a² + b² = c², where c is the hypotenuse—the side opposite the right angle. Show your working and include units. Give exact answers with square roots where needed, or round to 1 decimal place when asked.
Warm-up: Find the hypotenuse
The hypotenuse is the longest side of a right triangle.
1.Nathan checks a triangular sign for the pizza shop. Its perpendicular sides are 3 cm and 4 cm. Find the length of the hypotenuse.
2.Keira measures a right triangle with sides 5 m and 12 m meeting at a right angle. Which is its hypotenuse?
- 13 m
- 17 m
- √119 m
- 60 m
3.Tui says that side lengths 6, 8 and 10 make a right triangle. Is Tui correct? Show a calculation to support your answer.
On the delivery route: Find a missing side
Use a² + b² = c². Remember that the hypotenuse is c.
4.A delivery ramp forms a right triangle. The ramp is 13 m long, and its base is 5 m. How high does it reach?
5.A rectangular pizza box is 9 cm wide and 12 cm long. What is the length of the diagonal across its lid?
6.The diagonal of a rectangular menu board is 10 cm. One side is 6 cm. Find the length of the other side.
Challenge: Use the theorem in context
Sketch a right triangle if it helps you plan your solution.
7.A courier travels 8 km east, then 15 km north. What is the straight-line distance from the starting point to the destination?
8.A right triangle has a hypotenuse of 20 cm and one leg of 16 cm. Find its area. (Area = ½ × base × height.)
9.A square pizza has a diagonal of 10√2 cm. Find the length of one side and then its perimeter.
10.A right triangle has side lengths in the ratio 5:12:13. Its shortest side is 10 cm. Find the triangle’s area.
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