# How to Solve Pythagorean Theorem Problems? (+FREE Worksheet!)

In mathematics, the Pythagorean Theorem is the relationship between three sides of a right triangle.

## Related Topics

- How Calculate the Area of Trapezoids
- How to Find the volume and surface area of Rectangular Prisms
- How to Solve Triangles Problems
- How to Find Volume and Surface Area of Cubes
- How to Find the Perimeter of Polygons

## Step by step guide to solve Pythagorean Theorem problems

- We can use the Pythagorean Theorem to find a missing side in a right triangle.
- In any right triangle: \(\color{blue}{a^2+b^2= c^2}\)

**The Absolute Best Books to Ace Pre-Algebra to Algebra II**

### The Pythagorean Theorem – Example 1:

Right triangle ABC has two legs of lengths \(9\) cm (AB) and \(12\) cm (AC). What is the length of the third side (BC)?

**Solution**:

Use Pythagorean Theorem: \(\color{blue}{a^2+b^2= c^2}\)

Then: \(a^2+b^2= c^2 →9^2+12^2= c^2 →81+144=c^2\)

\(c^2=225 →\) \(c=\sqrt{225}=15\) \(cm\) → \(c=15 cm\)

### The Pythagorean Theorem – Example 2:

Find the hypotenuse of the following right triangle.

**Solution**:

Use Pythagorean Theorem: \(\color{blue}{a^2+b^2= c^2}\)

Then: \(a^2+b^2= c^2 →8^2+6^2= c^2 →64+36=c^2\)

\(c^2=100 →\) \(c=\sqrt{100}=10\) → \(c=10\)

### The Pythagorean Theorem – Example 3:

Find the hypotenuse of the following right triangle.

**Solution**:

Use Pythagorean Theorem: \(\color{blue}{a^2+b^2= c^2}\)

Then: \(a^2+b^2= c^2 →3^2+4^2= c^2 →9+16=c^2\)

\(c^2=25 →\) \(c=\sqrt{25}=5\) → \(c=5\)

** The Best Book to Help You Ace**** Pre-Algebra**

### The Pythagorean Theorem – Example 4:

Right triangle ABC has two legs of lengths \(6\) cm (AB) and \(8\) cm (AC). What is the length of the third side (BC)?

**Solution**:

Use Pythagorean Theorem: \(\color{blue}{a^2+b^2= c^2}\)

Then: \(a^2+b^2= c^2 →6^2+8^2= c^2 →36+64=c^2\)

\( c^2=100 →\) \(c=\sqrt{100}=10\) \(cm\) → \(c= 10 cm\)

## Exercises for Solveing the Pythagorean Theorem

### Find the missing side in each right triangle.

### Download Pythagorean Relationship Worksheet

- \(\color{blue}{13}\)
- \(\color{blue}{5}\)
- \(\color{blue}{15}\)
- \(\color{blue}{8}\)

**The Greatest Books for Students** **to Ace the Algebra**

## Related to This Article

### More math articles

- 6th Grade NHSAS Math Worksheets: FREE & Printable
- 10 Most Common 4th Grade MAP Math Questions
- Best Calculators for High School Algebra I
- Full-Length TSI Math Practice Test
- How to Use Models to Multiply Two Fractions?
- 10 Most Common PSAT 10 Math Questions
- A Comprehensive Collection of Free CBEST Math Practice Tests
- What time do SAT Scores Come out?
- Full-Length TABE 11 & 12 Math Practice Test
- FREE 8th Grade SBAC Math Practice Test

## What people say about "How to Solve Pythagorean Theorem Problems? (+FREE Worksheet!) - Effortless Math: We Help Students Learn to LOVE Mathematics"?

No one replied yet.