Right Triangle Solution: Find Side X Using 8 and 17 Units

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

The hypotenuse is always the longest side in a right triangle and sits opposite the right angle. In this problem, 17 is longer than 8, so 17 is the hypotenuse.

Q: Why do I get x² = 225 instead of x = 225?

When you solve $ x^2 = 225 $, you need to take the square root of both sides: $ x = \sqrt{225} = 15 $. Don't forget this final step!

Q: What if I get a negative answer when taking the square root?

Lengths are always positive in geometry! If you get $ x = \pm 15 $, only use the positive value: x = 15.

Q: Can I use the Pythagorean theorem on any triangle?

No! The Pythagorean theorem only works for right triangles (triangles with a 90° angle). Look for the right angle symbol in the diagram.

Q: What if my calculator gives me a decimal answer?

Sometimes the answer will be a decimal or involve $ \sqrt{} $. In this problem, $ \sqrt{225} $ is exactly 15, but other problems might give answers like $ \sqrt{50} $ or decimals.

Pythagorean Theorem with Given Hypotenuse

What is the length of the side marked X?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the length of side X

00:03 The triangle is right-angled, therefore we'll use the Pythagorean theorem

00:09 The sum of squares of the legs equals the square of the hypotenuse

00:12 We'll substitute the appropriate values according to the given data and solve for X

00:15 We'll isolate X

00:31 We'll take the square root

00:37 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the length of the side marked X?

Step-by-step solution

We use the Pythagorean theorem:

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

Final Answer

$15$

Key Points to Remember

Essential concepts to master this topic

Formula: For right triangles, $a^2 + b^2 = c^2$ where c is hypotenuse
Technique: Substitute known values: $8^2 + x^2 = 17^2$ gives $64 + x^2 = 289$
Check: Verify $8^2 + 15^2 = 64 + 225 = 289 = 17^2$ ✓

Common Mistakes

Avoid these frequent errors

Confusing which side is the hypotenuse
Don't assume the unknown side x is always the hypotenuse = using wrong formula setup! The hypotenuse is always the longest side, opposite the right angle. Always identify the hypotenuse first by finding the longest given side.

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

How do I know which side is the hypotenuse?

The hypotenuse is always the longest side in a right triangle and sits opposite the right angle. In this problem, 17 is longer than 8, so 17 is the hypotenuse.

Why do I get x² = 225 instead of x = 225?

When you solve $x^2 = 225$ , you need to take the square root of both sides: $x = \sqrt{225} = 15$ . Don't forget this final step!

What if I get a negative answer when taking the square root?

Lengths are always positive in geometry! If you get $x = \pm 15$ , only use the positive value: x = 15.

Can I use the Pythagorean theorem on any triangle?

No! The Pythagorean theorem only works for right triangles (triangles with a 90° angle). Look for the right angle symbol in the diagram.

What if my calculator gives me a decimal answer?

Sometimes the answer will be a decimal or involve $\sqrt{}$ . In this problem, $\sqrt{225}$ is exactly 15, but other problems might give answers like $\sqrt{50}$ or decimals.

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