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

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 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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