Calculate Rectangle Diagonal Segment BO: Given AB=8 and AD=6

Q: Why can I use the Pythagorean theorem on a rectangle?

A rectangle has four right angles, so the diagonal creates a right triangle with the length and width as legs. The diagonal becomes the hypotenuse, making the Pythagorean theorem perfect for this!

Q: What does it mean that diagonals bisect each other?

Bisect means cut in half. When diagonals intersect at point O, they split each other into two equal segments. So AO = OC and BO = OD.

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

Use the adjacent sides of the rectangle - the length and width that meet at a corner. In this problem, that's AB = 8 and AD = 6.

Q: Could I use BC and CD instead of AB and AD?

Yes! In a rectangle, opposite sides are equal, so BC = AD = 6 and CD = AB = 8. You'd get the same diagonal length of 10.

Q: What if I calculated AC as 14 by adding 8 + 6?

That's addition, not the Pythagorean theorem! You can't just add the sides. You must use $ \sqrt{8^2 + 6^2} $ because the diagonal forms the hypotenuse of a right triangle.

Rectangle Diagonals with Intersection Properties

Given the rectangle such that:

O is the intersection point of the diagonals of the rectangle.

Given: AD=6 , AB=8

Calculate the length of the section BO.

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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

Given the rectangle such that:

O is the intersection point of the diagonals of the rectangle.

Given: AD=6 , AB=8

Calculate the length of the section BO.

Step-by-step solution

To solve this problem, we'll utilize the properties of rectangles and the Pythagorean theorem:

Step 1: Determine the full diagonal of the rectangle using Pythagorean theorem: $AC = \sqrt{AB^2 + AD^2}$ .
Step 2: Since $O$ is the midpoint of the diagonal $AC$ , $BO = \frac{AC}{2}$ .

Now, let's calculate step-by-step:

Step 1: We know $AB = 8$ and $AD = 6$ , therefore, using the Pythagorean theorem:

$AC = \sqrt{AB^2 + AD^2} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10$

Step 2: Since the diagonals bisect each other, the length of $BO$ is half of $AC$ :

$BO = \frac{AC}{2} = \frac{10}{2} = 5$

Therefore, the solution to the problem is $BO = 5$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Pythagorean Rule: Rectangle diagonal equals square root of length squared plus width squared
Technique: Calculate $AC = \sqrt{8^2 + 6^2} = \sqrt{100} = 10$
Check: Diagonal segments equal half the full diagonal: BO = 10/2 = 5 ✓

Common Mistakes

Avoid these frequent errors

Forgetting that diagonals bisect each other
Don't calculate the full diagonal and think that's the answer = 10 instead of 5! The intersection point divides each diagonal into two equal parts. Always divide the full diagonal length by 2 to find any diagonal segment.

Practice Quiz

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Angle A is equal to 30°.
Angle B is equal to 60°.
Angle C is equal to 90°.

Can these angles form a triangle?

FAQ

Everything you need to know about this question

Why can I use the Pythagorean theorem on a rectangle?

A rectangle has four right angles, so the diagonal creates a right triangle with the length and width as legs. The diagonal becomes the hypotenuse, making the Pythagorean theorem perfect for this!

What does it mean that diagonals bisect each other?

Bisect means cut in half. When diagonals intersect at point O, they split each other into two equal segments. So AO = OC and BO = OD.

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

Use the adjacent sides of the rectangle - the length and width that meet at a corner. In this problem, that's AB = 8 and AD = 6.

Could I use BC and CD instead of AB and AD?

Yes! In a rectangle, opposite sides are equal, so BC = AD = 6 and CD = AB = 8. You'd get the same diagonal length of 10.

What if I calculated AC as 14 by adding 8 + 6?

That's addition, not the Pythagorean theorem! You can't just add the sides. You must use $\sqrt{8^2 + 6^2}$ because the diagonal forms the hypotenuse of a right triangle.

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Calculate Rectangle Diagonal Segment BO: Given AB=8 and AD=6

Rectangle Diagonals with Intersection Properties

❤️ 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 I use the Pythagorean theorem on a rectangle?

What does it mean that diagonals bisect each other?

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

Could I use BC and CD instead of AB and AD?

What if I calculated AC as 14 by adding 8 + 6?

🌟 Unlock Your Math Potential

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