The Pythagorean Theorem

The Pythagorean Theorem questions are often on the GED Math test.

This lesson is a part of Onsego GED Prep.

Please wait...

1. Determine the missing length in this right triangle using the Pythagorean theorem. Use this formula: \(a^{2} + b^{2} = c^{2} \)

\(b=12\)
\(c=15\)
\(a=?\)

A.\(9\: yd\)

B.\(27\: yd\)

C.\(45\: yd\)

Question 1 of 2

2. Determine the missing length in this right triangle using the Pythagorean theorem. Use this formula: \(a^{2} + b^{2} = c^{2} \)

\(a=12\)
\(b=16\)
\(c=?\)

A.\(400\; in\)

B.\(20\; in\)

C.\(200\; in\)

Question 2 of 2

 Loading...

 

Video Transcription

On the GED Math test, you might see a question about a triangle—but instead of being asked to find the area or perimeter, you’re asked to find the length of one of the sides.

For that, you’ll use the Pythagorean Theorem. You can find this formula on the GED Formula Sheet under the Algebra section.

Let’s take a look at how to use it.

What Is the Pythagorean Theorem?

In a right-angled triangle, the longest side—opposite the right angle—is called the hypotenuse. The two shorter sides are called legs.

The Pythagorean Theorem says that the square of the hypotenuse (c) is equal to the sum of the squares of the two legs (a and b):

a² + b² = c²

This means:
If you square the lengths of the two shorter sides and add them together, you’ll get the square of the longest side.

 Example: Finding the Hypotenuse

Let’s say one leg is 8 units and the other is 15 units. To find the hypotenuse, plug the numbers into the formula:

8² + 15² = c²
64 + 225 = c²
289 = c²

Now take the square root of both sides:

c = √289 = 17

So, the hypotenuse is 17 units long.

 What if You’re Missing a Shorter Side?

If you’re given the length of the hypotenuse and one leg, you still use the same formula:

a² + b² = c²

Just plug in the numbers you know and solve for x, the missing leg. Once you simplify the equation, take the square root at the end to find your answer.

 What to Expect on the GED Test

Sometimes the test won’t ask you to solve at all. Instead, you’ll just be asked to recognize the correct equation that matches a diagram or a short description. Let’s try one like that.

 Example Question:

Two hikers, Alex and Jordan, leave a campsite and walk in different directions that form a right angle, as shown in the diagram.

• Alex hikes 6 miles
• Jordan hikes 8 miles
• They can stay in contact if they are within 10 miles of each other

Which equation correctly represents this situation?

1. A) 6² + 8² = 10²
   B) 6² + 10² = 8²
   C) 8² + 10² = 6²
   D) 10² + 6² = 8²

 Explanation:

To solve this, you don’t need to calculate anything. Just match the numbers from the question to the formula:

a² + b² = c²

Here:

• The shorter sides are 6 and 8
• The longest side—the hypotenuse—is 10

So the correct setup is:

6² + 8² = 10²

That matches answer A.

Recap:

• Use a² + b² = c² for any right triangle
• a and b are the legs (shorter sides)
• c is the hypotenuse (the longest side)
• You might solve for a missing side, or just recognize the correct equation
• Either way, focus on plugging in the right numbers and identifying the correct structure

Last Updated on October 20, 2025.