Calculate Rectangle Diagonal: Finding AC Length in 3×4 Rectangle

Q: How do I know which sides to use in the Pythagorean theorem?

Use the two adjacent sides that meet at a corner. In this case, AD = 3 and AB = 4 meet at point A, and the diagonal AC connects the opposite corners.

Q: Do all rectangles work the same way for diagonals?

Yes! Every rectangle has two equal diagonals, and both can be found using the Pythagorean theorem with any pair of adjacent sides.

Q: How can I check if my diagonal length is reasonable?

The diagonal should be longer than either side but shorter than the sum of both sides. Here: 4

Pythagorean Theorem with Rectangle Diagonals

Look at the rectangle ABC is below.

AB = 4

AD = 3

Determine the length of the diagonal AC?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate AC

00:03 Opposite sides are equal in a rectangle

00:07 Side values according to the given data

00:11 Opposite sides are equal in a rectangle

00:15 Side values according to the given data

00:21 We'll use the Pythagorean theorem in triangle ABC

00:32 We'll substitute appropriate values and solve for AC

00:41 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

Look at the rectangle ABC is below.

AB = 4

AD = 3

Determine the length of the diagonal AC?

Step-by-step solution

In a rectangle, each pair of opposite sides are equal to each other, therefore:

$AB=DC=4$

We will use the Pythagorean theorem to find AC:

$AC^2=BC^2+DC^2$

Let's substitute the known data:

$AC^2=3^2+4^2$

$AC^2=9+16$

$AC^2=25$

Let's take the square root:

$AC=\sqrt{25}=5$

Final Answer

$5$

Key Points to Remember

Essential concepts to master this topic

Rule: Rectangle diagonal forms right triangle with adjacent sides
Technique: Apply $c^2 = a^2 + b^2$ where AC = diagonal, AD = 3, AB = 4
Check: Verify $5^2 = 3^2 + 4^2$ gives 25 = 9 + 16 = 25 ✓

Common Mistakes

Avoid these frequent errors

Adding side lengths instead of using Pythagorean theorem
Don't simply add 3 + 4 = 7 for the diagonal! This gives the wrong answer because diagonals don't equal the sum of sides. Always use $c^2 = a^2 + b^2$ to find the diagonal of a rectangle.

Practice Quiz

Test your knowledge with interactive questions

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

Everything you need to know about this question

Why can't I just add the two sides to get the diagonal?

A diagonal cuts across the rectangle at an angle, not along the edges. It's the hypotenuse of a right triangle, which is always longer than either side but shorter than their sum.

How do I know which sides to use in the Pythagorean theorem?

Use the two adjacent sides that meet at a corner. In this case, AD = 3 and AB = 4 meet at point A, and the diagonal AC connects the opposite corners.

What if I get a decimal or square root answer?

That's normal! Many diagonals are irrational numbers. If you get $\sqrt{25}$ , simplify to 5. If you get $\sqrt{13}$ , leave it as is or use a calculator for the decimal.

Do all rectangles work the same way for diagonals?

Yes! Every rectangle has two equal diagonals, and both can be found using the Pythagorean theorem with any pair of adjacent sides.

How can I check if my diagonal length is reasonable?

The diagonal should be longer than either side but shorter than the sum of both sides. Here: 4 < 5 < 7, so our answer of 5 makes sense!

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