Calculate the Hypotenuse X in a 3-4 Right Triangle using Pythagorean Theorem

Q: How do I know which side is the hypotenuse?

The hypotenuse is always the longest side and it's opposite the right angle. In this triangle, X is opposite the right angle, so it's the hypotenuse.

Q: What if I forget to take the square root at the end?

You'll get $ c^2 = 25 $ but forget that c = 5. Always remember: after finding $ c^2 $, take the square root to find the actual length!

Q: Why is this called a 3-4-5 triangle?

This is one of the most famous Pythagorean triples - whole numbers that satisfy the theorem. Other common ones include 5-12-13 and 8-15-17!

Q: Can I use this formula for any triangle?

Only for right triangles! The triangle must have a 90-degree angle. For other triangles, you need different formulas like the Law of Cosines.

Pythagorean Theorem with Classic Triangle

What is the length of the hypotenuse?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the length of hypotenuse X

00:03 Use the Pythagorean theorem in a right triangle

00:07 The sum of squares of both legs equals the square of hypotenuse

00:11 Substitute appropriate values and solve for X

00:21 Extract the root

00:27 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the length of the hypotenuse?

Step-by-step solution

We use the Pythagorean theorem

$AC^2+AB^2=BC^2$

We insert the known data:

$3^2+4^2=BC^2$

$9+16=BC^2$

$25=BC^2$

We extract the root:

$\sqrt{25}=BC$

$5=BC$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: For right triangles: $a^2 + b^2 = c^2$
Technique: Substitute known sides: $3^2 + 4^2 = 9 + 16 = 25$
Check: Verify $5^2 = 25$ matches our result ✓

Common Mistakes

Avoid these frequent errors

Adding the legs instead of squaring them
Don't add 3 + 4 = 7! This ignores the squares completely and gives a wrong hypotenuse. The legs must be squared first, then added: $3^2 + 4^2 = 25$ . Always square each leg before adding.

Practice Quiz

Test your knowledge with interactive questions

Consider a right-angled triangle, AB = 8 cm and AC = 6 cm.
Calculate the length of side BC.

FAQ

Everything you need to know about this question

Why do we square the sides in the Pythagorean theorem?

The Pythagorean theorem is based on the relationship between the areas of squares built on each side. When we square a side length, we're finding the area of that square!

How do I know which side is the hypotenuse?

The hypotenuse is always the longest side and it's opposite the right angle. In this triangle, X is opposite the right angle, so it's the hypotenuse.

What if I forget to take the square root at the end?

You'll get $c^2 = 25$ but forget that c = 5. Always remember: after finding $c^2$ , take the square root to find the actual length!

Why is this called a 3-4-5 triangle?

This is one of the most famous Pythagorean triples - whole numbers that satisfy the theorem. Other common ones include 5-12-13 and 8-15-17!

Can I use this formula for any triangle?

Only for right triangles! The triangle must have a 90-degree angle. For other triangles, you need different formulas like the Law of Cosines.

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Calculate the Hypotenuse X in a 3-4 Right Triangle using Pythagorean Theorem

Pythagorean Theorem with Classic Triangle

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do we square the sides in the Pythagorean theorem?

How do I know which side is the hypotenuse?

What if I forget to take the square root at the end?

Why is this called a 3-4-5 triangle?

Can I use this formula for any triangle?

🌟 Unlock Your Math Potential

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