c² = a² + b²: Error Analysis & Misconceptions
Mathematics
Grade 7
12 questions
~24 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on identifying and correcting misconceptions related to the formula c² = a² + b² in Pythagoras Theorem, including practice, reasoning, real-world problems, and error analysis.
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c² = a² + b²: Error Analysis & Misconceptions
Subject: MathematicsGrade: Grade 7
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Untitled Worksheet
Grade Grade 7
A
Fluency & Practice
Calculate the missing side length or hypotenuse in each triangle. Show your working in the grid spaces provided.
1.
A right-angled triangle has legs of 6 cm and 8 cm. Find the length of the hypotenuse c.
[2 marks]2.
In a triangle, the hypotenuse c is 13 units, and one leg a is 5 units. Find the other leg b.
[2 marks]3.
Calculate c if a = 9 and b = 12.
[2 marks]B
Problem Solving & Reasoning
Solve the following multi-step problems. Explain your reasoning clearly.
1.
A ladder leans against a wall forming a right triangle. The ladder is 15 meters long, and the base of the ladder is 9 meters from the wall. Find the height the ladder reaches on the wall.
[3 marks]2.
A rectangular garden has a diagonal of 25 meters. One side measures 7 meters. Find the length of the other side.
[3 marks]C
Real-world Applications
Apply c² = a² + b² to solve real-life problems.
1.
A television screen measures 48 inches diagonally. The width of the screen is 40 inches. Find the height of the screen.
[2 marks]D
Challenge & Extension
Attempt these more difficult problems to extend your understanding.
1.
A right triangle has a hypotenuse of 20 units. The difference between the legs is 4 units. Find the lengths of both legs.
[3 marks]2.
Construct a right triangle where the hypotenuse is 10 cm, and one leg is 6 cm. Draw and verify the other leg on the grid.
[3 marks]E
Mixed Review
Answer the variety of questions below to review your understanding of c² = a² + b².
1.
True or False: If a triangle has sides 3, 4, and 6, it is a right triangle. Justify your answer.
[1 mark]2.
Identify the common mistake: A student calculates c² = a² + b² but gets a wrong answer because they swapped the values of a and b. How can this mistake be avoided?
[2 marks]F
Error Analysis & Misconceptions
Review the errors below and identify the mistake. Then, correct the solution.
1.
A student claims that if one leg is 5 and the hypotenuse is 13, then the other leg must be 12. The student calculates 13² = 5² + x² and finds x = 12. Identify the mistake if any.
[2 marks]2.
A student incorrectly applies the formula as c² = a² - b². Explain why this is wrong and what the correct formula is.
[2 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet