Calculate Rectangle Diagonal Length: Finding BD When AB=4 and AD=3

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

Because the diagonal is the hypotenuse of a right triangle, not a straight path along the sides! The diagonal cuts across the rectangle, creating a shorter path than going around two sides.

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

Use the two sides that meet at a right angle (90°). In rectangle ABCD, if you want diagonal BD, use the two sides that connect to either B or D: AB and AD.

Q: Does it matter which diagonal I calculate?

No! In a rectangle, both diagonals are exactly the same length. So BD = AC always. You can calculate either one using the same method.

Q: Can I use this method for any quadrilateral?

Only for rectangles and squares! Other quadrilaterals don't necessarily have right angles at the corners, so the Pythagorean theorem won't work.

Pythagorean Theorem with Rectangle Diagonals

Given the rectangle ABCD

It is known that:

AB=4

AD=3

What is the length of the diagonal BD?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find diagonal BD

00:04 Side values according to the given data

00:13 We'll use the Pythagorean theorem in triangle ABD

00:22 We'll substitute appropriate values and solve for BD

00:31 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

Given the rectangle ABCD

It is known that:

AB=4

AD=3

What is the length of the diagonal BD?

Step-by-step solution

We will use the Pythagorean theorem in order to find BD:

$BD^2=AD^2+AB^2$

Let's input the known data:

$BD^2=3^2+4^2$

$BD^2=9+16$

$BD^2=25$

We'll take the square root:

$BD=\sqrt{25}=5$

Final Answer

$5$

Key Points to Remember

Essential concepts to master this topic

Rule: Rectangle diagonals form right triangles with adjacent sides
Technique: Use $d^2 = l^2 + w^2$ where d is diagonal
Check: Verify $5^2 = 3^2 + 4^2 = 9 + 16 = 25$ ✓

Common Mistakes

Avoid these frequent errors

Adding side lengths instead of using Pythagorean theorem
Don't calculate BD = AB + AD = 4 + 3 = 7! This gives the perimeter of two sides, not the diagonal length. The diagonal creates a right triangle, so you need squares. Always use $BD^2 = AB^2 + AD^2$ and take the square root.

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?

Because the diagonal is the hypotenuse of a right triangle, not a straight path along the sides! The diagonal cuts across the rectangle, creating a shorter path than going around two sides.

How do I know which sides to use in the formula?

Use the two sides that meet at a right angle (90°). In rectangle ABCD, if you want diagonal BD, use the two sides that connect to either B or D: AB and AD.

What if I get a decimal or square root answer?

That's normal! Many diagonals aren't whole numbers. If you get $\sqrt{26}$ , you can leave it as a square root or calculate the decimal approximation depending on what the problem asks.

Does it matter which diagonal I calculate?

No! In a rectangle, both diagonals are exactly the same length. So BD = AC always. You can calculate either one using the same method.

Can I use this method for any quadrilateral?

Only for rectangles and squares! Other quadrilaterals don't necessarily have right angles at the corners, so the Pythagorean theorem won't work.

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Calculate Rectangle Diagonal Length: Finding BD When AB=4 and AD=3

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

How do I know which sides to use in the formula?

What if I get a decimal or square root answer?

Does it matter which diagonal I calculate?

Can I use this method for any quadrilateral?

🌟 Unlock Your Math Potential

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