Triangle Height Calculation: Finding X When Area = 3 and Base = 2

Q: Why do I need to multiply by 2 when finding height?

The area formula has 1/2 in it: Area = (1/2) × base × height. To isolate height, you must undo that 1/2 by multiplying both sides by 2 first!

Q: Which side of the triangle is the base?

The base is the side that the height is perpendicular to. In this problem, the base is labeled as 2 and runs horizontally along the bottom of the triangle.

Q: What exactly is the height of a triangle?

The height is the perpendicular distance from the base to the opposite vertex. It forms a 90° angle with the base, shown as the vertical line labeled x in this diagram.

Q: How do I know if I'm using the right formula?

For any triangle, Area = (1/2) × base × height always works! Just make sure your height is perpendicular to your chosen base.

Q: Can I use a different side as the base?

Yes! But then you'd need the height perpendicular to that side. The area will be the same no matter which base-height pair you choose.

Triangle Area Formula with Height Finding

The area of the triangle below is equal to 3.

Calculate X.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find the height, X.

00:07 We'll use the area formula for triangles.

00:11 That's base B C times height A E, then divide by 2.

00:17 Now, plug in the numbers and solve for height, X.

00:26 Remember to simplify by reducing the 2.

00:30 Great job! That's how we find the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The area of the triangle below is equal to 3.

Calculate X.

Step-by-step solution

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

Step 1: Identify the given information.
Step 2: Apply the formula for the area of a triangle.
Step 3: Solve for $X$ .

Now, let's work through each step:
Step 1: The problem provides the area of the triangle as $3$ square units, with the base of the triangle as $2$ units.
Step 2: The formula used for the area of a triangle is $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ .
Given that the base is $2$ and the area is $3$ , we rearrange to find $X$ (the height):

$3 = \frac{1}{2} \times 2 \times X$

Simplifying, we get:

$3 = X$

Therefore, the length of $X$ is $3$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Area Formula: Area = (1/2) × base × height for triangles
Rearrangement: Height = (2 × Area) ÷ base = (2 × 3) ÷ 2 = 3
Verification: Check: (1/2) × 2 × 3 = 3 square units ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by 2 when solving for height
Don't just divide Area by base = 3 ÷ 2 = 1.5! This ignores the 1/2 factor in the formula and gives the wrong height. Always remember to multiply Area by 2 first, then divide by base.

Practice Quiz

Test your knowledge with interactive questions

Calculate the area of the triangle using the data in the figure below.

FAQ

Everything you need to know about this question

Why do I need to multiply by 2 when finding height?

The area formula has 1/2 in it: Area = (1/2) × base × height. To isolate height, you must undo that 1/2 by multiplying both sides by 2 first!

Which side of the triangle is the base?

The base is the side that the height is perpendicular to. In this problem, the base is labeled as 2 and runs horizontally along the bottom of the triangle.

What exactly is the height of a triangle?

The height is the perpendicular distance from the base to the opposite vertex. It forms a 90° angle with the base, shown as the vertical line labeled x in this diagram.

How do I know if I'm using the right formula?

For any triangle, Area = (1/2) × base × height always works! Just make sure your height is perpendicular to your chosen base.

Can I use a different side as the base?

Yes! But then you'd need the height perpendicular to that side. The area will be the same no matter which base-height pair you choose.

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