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Pythagorean Triples Find Hypotenuse cc = √(a²+b²)Find Missing Leg Master Generator

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Set A • 8 Qs

PanMaths.comFinding the Hypotenuse Worksheet Generator with Answers (c = √(a² + b²)) • Set A (Medium)

Name: __________________________

Date: _____________ Period: ____

Score: _____ / 8

1.FIND HYPOTENUSE c

c =

2.FIND HYPOTENUSE c

c =

3.FIND HYPOTENUSE c

c =

4.FIND HYPOTENUSE c

c =

5.FIND HYPOTENUSE c

c =

6.FIND HYPOTENUSE c

c =

7.FIND HYPOTENUSE c

c =

8.FIND HYPOTENUSE c

c =

PanMaths.com • Free Math Worksheet Generator • Set A (Medium)Page 1 of 2

PanMaths.comAnswer Key & Worked Solutions • Set A (Medium)

Answer Key

Total Problems: 8

1.FIND HYPOTENUSE c

c =15

1. Pythagorean Theorem: a² + b² = c² (for right triangles)

2. Substitute Legs: 9² + 12² = c²

3. Calculate Squares: 81 + 144 = 225 = c²

2.FIND HYPOTENUSE c

c =20

1. Pythagorean Theorem: a² + b² = c² (for right triangles)

2. Substitute Legs: 12² + 16² = c²

3. Calculate Squares: 144 + 256 = 400 = c²

3.FIND HYPOTENUSE c

c =17

1. Pythagorean Theorem: a² + b² = c² (for right triangles)

2. Substitute Legs: 8² + 15² = c²

3. Calculate Squares: 64 + 225 = 289 = c²

4.FIND HYPOTENUSE c

c =10

1. Pythagorean Theorem: a² + b² = c² (for right triangles)

2. Substitute Legs: 6² + 8² = c²

3. Calculate Squares: 36 + 64 = 100 = c²

5.FIND HYPOTENUSE c

c =13

1. Pythagorean Theorem: a² + b² = c² (for right triangles)

2. Substitute Legs: 5² + 12² = c²

3. Calculate Squares: 25 + 144 = 169 = c²

6.FIND HYPOTENUSE c

c =29

1. Pythagorean Theorem: a² + b² = c² (for right triangles)

2. Substitute Legs: 20² + 21² = c²

3. Calculate Squares: 400 + 441 = 841 = c²

7.FIND HYPOTENUSE c

c =26

1. Pythagorean Theorem: a² + b² = c² (for right triangles)

2. Substitute Legs: 10² + 24² = c²

3. Calculate Squares: 100 + 576 = 676 = c²

8.FIND HYPOTENUSE c

c =17

1. Pythagorean Theorem: a² + b² = c² (for right triangles)

2. Substitute Legs: 8² + 15² = c²

3. Calculate Squares: 64 + 225 = 289 = c²

PanMaths.com • Answer Key & Worked SolutionsPage 2 of 2

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Worksheet Info

Categorygeometry

Grade LevelGrades 7-9 (Pre-Algebra & Geometry)

DifficultyFoundational to Intermediate (Calculating c given legs a and b)

Time15-20 min

Skills Practiced

✓ Applying the Pythagorean formula c = √(a² + b²)
✓ Squaring side lengths accurately
✓ Summing squares of legs (a² + b²)
✓ Evaluating square roots of sums
✓ Reading right triangle diagrams and locating the hypotenuse opposite 90°

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Step-by-Step Method to Calculate the Hypotenuse

Follow these 4 reliable steps on every problem:

Step 1 (Formula): Write the Pythagorean Theorem: c² = a² + b².
Step 2 (Substitute): Replace a and b with the given leg lengths (e.g. if a = 6 and b = 8, then c² = 6² + 8²).
Step 3 (Simplify): Evaluate the exponents and add: c² = 36 + 64 = 100.
Step 4 (Square Root): Take the principal square root: c = √100 = 10.

The #1 Error: √(a² + b²) ≠ a + b

The single most frequent mistake made by students is attempting to cancel the square root with the squares before adding: e.g. incorrectly thinking √(3² + 4²) = 3 + 4 = 7.

Demonstrating with numbers proves why this is mathematically invalid: √(9 + 16) = √25 = 5, which does not equal 7! The addition inside the radical must be completed before extracting the root.

Anti-Cheat Classroom Versions & Step-by-Step Answer Keys

PanMaths supports busy teachers by generating twin anti-cheat versions: Set A and Set B. Both sets maintain identical difficulty while randomizing numerical dimensions across adjacent student desks. The generated answer key details the substitution line, sum of squares, and final radical evaluation for quick 60-second grading.