Calculate Triangle Perimeter: 15×8 Rectangle with Diagonal

Q: Why can't I just add all the rectangle sides to get the triangle perimeter?

A triangle has only 3 sides, not 4! Triangle ABD uses two sides of the rectangle (AB=15, AD=8) plus the diagonal BD, not all four rectangle sides.

Q: How do I know which sides form the triangle?

Look at the three vertices mentioned: A, B, and D. Connect these points to see the triangle. The sides are AB, AD, and the diagonal BD.

Q: Why do I need the Pythagorean theorem here?

The diagonal BD creates a right triangle with the rectangle sides. Since we know AB=15 and AD=8, we can find BD using $ c^2 = a^2 + b^2 $.

Q: How can I check if my triangle perimeter is reasonable?

The triangle perimeter should be less than the rectangle perimeter (46). Since 40

Triangle Perimeter with Pythagorean Theorem

Look at the following rectangle:

Calculate the perimeter of the triangle ABD.

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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

Look at the following rectangle:

Calculate the perimeter of the triangle ABD.

Step-by-step solution

To solve the problem of finding the perimeter of triangle ABD, we will apply the following steps:

Step 1: Identify the given dimensions of the rectangle.
Step 2: Calculate the length of the diagonal BD using the Pythagorean theorem.
Step 3: Sum the sides of triangle ABD to find its perimeter.

Now, let's work through each step:

Step 1: We know from the problem that AB = 15 and AD = 8.

Step 2: The triangle ABD is a right triangle with AB and AD as the legs, and BD as the hypotenuse. Therefore, by the Pythagorean theorem:

BD^2 = AB^2 + AD^2 = 15^2 + 8^2

Calculating these squares gives:

BD^2 = 225 + 64 = 289

Taking the square root of both sides, we find:

BD = \sqrt{289} = 17

Step 3: Now, calculate the perimeter of triangle ABD.

\text{Perimeter of ABD} = AB + AD + BD = 15 + 8 + 17 = 40

Therefore, the perimeter of triangle ABD is $40$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rectangle Properties: Opposite sides equal, all angles 90 degrees
Pythagorean Theorem: $BD = \sqrt{15^2 + 8^2} = \sqrt{289} = 17$
Verification: Check diagonal calculation: $15^2 + 8^2 = 225 + 64 = 289$ ✓

Common Mistakes

Avoid these frequent errors

Adding rectangle dimensions instead of calculating diagonal
Don't just add 15 + 8 + (15+8) = 46! This treats the diagonal as if it equals the sum of two sides, which violates geometry. The diagonal is always shorter than the sum of two sides. Always use the Pythagorean theorem to find the diagonal length.

Practice Quiz

Test your knowledge with interactive questions

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't I just add all the rectangle sides to get the triangle perimeter?

A triangle has only 3 sides, not 4! Triangle ABD uses two sides of the rectangle (AB=15, AD=8) plus the diagonal BD, not all four rectangle sides.

How do I know which sides form the triangle?

Look at the three vertices mentioned: A, B, and D. Connect these points to see the triangle. The sides are AB, AD, and the diagonal BD.

Why do I need the Pythagorean theorem here?

The diagonal BD creates a right triangle with the rectangle sides. Since we know AB=15 and AD=8, we can find BD using $c^2 = a^2 + b^2$ .

What if I get a decimal answer for the diagonal?

That's normal! Many diagonals aren't whole numbers. In this problem, $\sqrt{289} = 17$ works out perfectly, but always use a calculator if needed and round appropriately.

How can I check if my triangle perimeter is reasonable?

The triangle perimeter should be less than the rectangle perimeter (46). Since 40 < 46, our answer makes sense! The triangle uses a shortcut (diagonal) instead of two full sides.

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Calculate Triangle Perimeter: 15×8 Rectangle with Diagonal

Triangle Perimeter with Pythagorean Theorem

❤️ 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 all the rectangle sides to get the triangle perimeter?

How do I know which sides form the triangle?

Why do I need the Pythagorean theorem here?

What if I get a decimal answer for the diagonal?

How can I check if my triangle perimeter is reasonable?

🌟 Unlock Your Math Potential

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