Rectangle Side Length: Using Pythagorean Theorem with AC=13 and AB=12

Q: Why is AC the hypotenuse and not a leg?

In any rectangle, the diagonal is always the longest side and forms the hypotenuse of a right triangle. The diagonal AC connects opposite corners, making it longer than any side like AB or BC.

Q: How do I know which sides are legs?

The legs are the two sides of the rectangle that meet at a right angle. In this problem, AB and BC are legs because they form the 90° corner of rectangle ABCD.

Q: What if I get a negative number under the square root?

This means you made an error! In rectangles, $ c^2 $ (diagonal squared) is always larger than $ a^2 $ (any side squared). Double-check that you're using the diagonal as the hypotenuse.

Q: How can I verify my answer is correct?

Square all three values and check: $ 12^2 + 5^2 = 144 + 25 = 169 $ and $ 13^2 = 169 $. When they're equal, you're right!

Pythagorean Theorem with Rectangle Diagonals

ABCD is a rectangle.

AC = 13

AB = 12

Calculate the length of the side BC.

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Step-by-step video solution

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Step-by-step written solution

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Understand the problem

ABCD is a rectangle.

AC = 13

AB = 12

Calculate the length of the side BC.

Step-by-step solution

When writing the name of a polygon, the letters will always be in the order of the sides:

This is a rectangle ABCD:

This is a rectangle ABDC:

Always go in order, and always with the right corner to the one we just mentioned.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rectangle Property: Diagonals connect opposite corners forming right triangles
Pythagorean Formula: $a^2 + b^2 = c^2$ where c is diagonal
Check: Verify $12^2 + 5^2 = 144 + 25 = 169 = 13^2$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting that diagonal is the hypotenuse
Don't use AC = 13 as a leg in the formula $13^2 + 12^2 = BC^2$ = wrong answer 17! The diagonal is always the longest side (hypotenuse) in a rectangle. Always use diagonal as c: $12^2 + BC^2 = 13^2$ .

Practice Quiz

Test your knowledge with interactive questions

Look at the triangle in the diagram. How long is side AB?

FAQ

Everything you need to know about this question

Why is AC the hypotenuse and not a leg?

In any rectangle, the diagonal is always the longest side and forms the hypotenuse of a right triangle. The diagonal AC connects opposite corners, making it longer than any side like AB or BC.

How do I know which sides are legs?

The legs are the two sides of the rectangle that meet at a right angle. In this problem, AB and BC are legs because they form the 90° corner of rectangle ABCD.

Can I use any corner for the right triangle?

Yes! Every corner of a rectangle creates a right triangle with the diagonal. You could use triangle ABC, ACD, BDC, or ABD - they all give the same relationships.

What if I get a negative number under the square root?

This means you made an error! In rectangles, $c^2$ (diagonal squared) is always larger than $a^2$ (any side squared). Double-check that you're using the diagonal as the hypotenuse.

How can I verify my answer is correct?

Square all three values and check: $12^2 + 5^2 = 144 + 25 = 169$ and $13^2 = 169$ . When they're equal, you're right!

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Rectangle Side Length: Using Pythagorean Theorem with AC=13 and AB=12

Pythagorean Theorem with Rectangle Diagonals

❤️ 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 is AC the hypotenuse and not a leg?

How do I know which sides are legs?

Can I use any corner for the right triangle?

What if I get a negative number under the square root?

How can I verify my answer is correct?

🌟 Unlock Your Math Potential

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