Rectangle Side Length: Using Pythagorean Theorem with AC=13 and AB=12
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
Step-by-step written solution
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
5
Key Points to Remember
- Rectangle Property: Diagonals connect opposite corners forming right triangles
- Pythagorean Formula: where c is diagonal
- Check: Verify ✓
Common Mistakes
- Forgetting that diagonal is the hypotenuse Don't use AC = 13 as a leg in the formula = wrong answer 17! The diagonal is always the longest side (hypotenuse) in a rectangle. Always use diagonal as c: .
Practice Quiz
The points A and O are shown in the figure below.
Is it possible to draw a rectangle so that the side AO is its diagonal?
FAQ
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, (diagonal squared) is always larger than (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: and . When they're equal, you're right!
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