a² = c² - b²: Problem Solving & Reasoning
Mathematics
Grade 6
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on solving for the shorter side 'a' in the formula a² = c² - b², involving procedural and reasoning skills suitable for Grade 6 students.
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a² = c² - b²: Problem Solving & Reasoning
Subject: MathematicsGrade: Grade 6
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Untitled Worksheet
Grade Grade 6
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the length of side a, given that c = 13 and b = 5 in a right-angled triangle using the formula a² = c² - b².
[3 marks]2.
A ladder leaning against a wall has a height of 9 meters and the base is 7 meters from the wall. Calculate the length of the ladder using a² = c² - b², where c is the hypotenuse.
[4 marks]3.
In a triangle, the hypotenuse c is 15 units and side b is 9 units. Find side a.
[3 marks]4.
A rectangular garden has a diagonal of 17 meters and one side of 8 meters. Find the length of the other side using the formula a² = c² - b².
[4 marks]5.
Construct a right-angled triangle on the grid where the hypotenuse c is 10 units and side b is 6 units. Measure and record the length of side a.
[4 marks]6.
A tree casts a shadow of 12 meters when the sun's angle produces a hypotenuse of 15 meters in the triangle formed. Find the height of the tree (side a).
[4 marks]7.
Determine side a if c = 20 and b = 16, using the formula a² = c² - b².
[3 marks]8.
A ramp forms a right triangle with hypotenuse 25 meters and one side 15 meters. Calculate the length of the shorter side.
[4 marks]9.
Identify and correct the mistake in the following statement: 'If c = 10 and b = 6, then a = 4 because a² = c² - b².'
[2 marks]10.
Using the grid, construct a right triangle where c = 13 units and b = 5 units. Calculate and record the length of side a.
[4 marks]11.
Challenge: Given c = 25 and b = 7, solve for side a. Then, verify your result by calculating a² and confirming it equals c² - b².
[4 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet