Triangle Perimeter Calculation: Finding the Sum of Sides 7, 8, and 14

Q: What's the difference between perimeter and area?

Perimeter is the distance around the outside of a shape (like walking around a fence). Area is the space inside the shape (like grass inside the fence). For perimeter, just add the sides!

Q: Do I need to know what type of triangle this is?

No! The perimeter formula P = a + b + c works for any triangle - scalene, isosceles, equilateral, right, or obtuse. Just add the three side lengths.

Q: How can I check if these sides actually make a triangle?

Use the triangle inequality theorem: the sum of any two sides must be greater than the third side. Check: 7 + 8 = 15 > 14 ✓, 7 + 14 = 21 > 8 ✓, 8 + 14 = 22 > 7 ✓

Q: What if I accidentally use the wrong sides?

Always identify each side carefully from the diagram. In this problem: AB = 7, BC = 14, CA = 8. Double-check by looking at which number is near which side of the triangle.

Q: Can perimeter ever be negative or zero?

Never! Side lengths are always positive numbers, so perimeter is always positive. If you get zero or negative, check your arithmetic or make sure you're adding (not subtracting) the sides.

Perimeter Calculation with Integer Side Lengths

Find the perimeter of the triangle ABC

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine the perimeter of the triangle

00:03 The perimeter of the triangle equals the sum of its sides

00:07 Substitute in the relevant values according to the given data and solve for the perimeter

00:12 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Find the perimeter of the triangle ABC

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given information.
Step 2: Apply the perimeter formula for a triangle.
Step 3: Perform the addition to find the perimeter.

Now, let's work through each step:

Step 1: We have the lengths of the sides of $\triangle ABC$ as follows:
$AB = 7$ , $BC = 14$ , and $CA = 8$ .

Step 2: We'll use the formula for the perimeter of a triangle, which is the sum of its side lengths:
$P = AB + BC + CA$ .

Step 3: Plugging in the values, we calculate:
$P = 7 + 14 + 8 = 29$ .

Therefore, the perimeter of $\triangle ABC$ is $\textbf{29}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Perimeter equals the sum of all three triangle sides
Formula: P = a + b + c where sides are 7 + 14 + 8
Check: Verify triangle inequality: 7 + 8 > 14, 7 + 14 > 8, 8 + 14 > 7 ✓

Common Mistakes

Avoid these frequent errors

Using area formula instead of perimeter
Don't use base × height ÷ 2 = 56 ÷ 2 = 28! That's the area formula, not perimeter. Perimeter measures distance around the outside, not space inside. Always add all three side lengths for perimeter.

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

What's the difference between perimeter and area?

Perimeter is the distance around the outside of a shape (like walking around a fence). Area is the space inside the shape (like grass inside the fence). For perimeter, just add the sides!

Do I need to know what type of triangle this is?

No! The perimeter formula P = a + b + c works for any triangle - scalene, isosceles, equilateral, right, or obtuse. Just add the three side lengths.

How can I check if these sides actually make a triangle?

Use the triangle inequality theorem: the sum of any two sides must be greater than the third side. Check: 7 + 8 = 15 > 14 ✓, 7 + 14 = 21 > 8 ✓, 8 + 14 = 22 > 7 ✓

What if I accidentally use the wrong sides?

Always identify each side carefully from the diagram. In this problem: AB = 7, BC = 14, CA = 8. Double-check by looking at which number is near which side of the triangle.

Can perimeter ever be negative or zero?

Never! Side lengths are always positive numbers, so perimeter is always positive. If you get zero or negative, check your arithmetic or make sure you're adding (not subtracting) the sides.

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