Pythagoras Triangle Problem Solving

Name:

Date:

Right-angled triangle with Pythagorean theorem

📚 Part 1: Multiple Choice

Instructions: Choose the best answer for each question.

1. In a right-angled triangle, the longest side is called the:

Adjacent side

Opposite side

Hypotenuse

Base

2. The Pythagorean theorem states that:

a + b = c

a² + b² = c²

a × b = c

a² + b = c²

3. A triangle has sides of 3 cm, 4 cm, and 5 cm. This is:

Not a right-angled triangle

A right-angled triangle

An impossible triangle

An equilateral triangle

✏️ Part 2: Problem Solving

Instructions: Use the Pythagorean theorem (a² + b² = c²) to solve these problems. Show your working.

4. Find the length of the hypotenuse if the two shorter sides are 6 cm and 8 cm.

Answer: _____________ cm

5. 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?

Answer: _____________ metres

6. A rectangular park is 120 metres long and 90 metres wide. What is the shortest distance from one corner to the opposite corner?

Answer: _____________ metres

7. A builder needs to check if a corner of a house is square. They measure 4 metres along one wall and 3 metres along the other wall. What should the diagonal measurement be if the corner is perfectly square?

Answer: _____________ metres

🏗️ Part 3: Challenge Problem

Instructions: Read the problem carefully and show all your working.

8. Fencing Challenge: Mrs. Chen owns a triangular block of land. Two sides of her property are 80 metres and 60 metres long, and they meet at a right angle. She wants to put a fence around the entire property. If fencing costs $45 per metre, how much will it cost to fence her entire property?

Step 1: Find the length of the third side (hypotenuse)

Step 2: Calculate the total perimeter

Step 3: Calculate the total cost

Final Answer: The total cost will be $_______________