Find X: Triangle with Area 15 and Base 3

Q: Why do triangles have that 1/2 in the area formula?

A triangle is exactly half of a rectangle! If you draw a rectangle with the same base and height, then draw a diagonal, you get two identical triangles. That's why we multiply by 1/2.

Q: What if the triangle looks different from this one?

The formula $ A = \frac{1}{2} \times base \times height $ works for any triangle! The height is always the perpendicular distance from the base to the opposite vertex.

Q: How do I solve 15 = (3/2) × x step by step?

Multiply both sides by the reciprocal $ \frac{2}{3} $:$ 15 \times \frac{2}{3} = x $$ \frac{30}{3} = 10 $

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

Yes! You can pick any side as the base, but then the height must be perpendicular to that base. The area will always come out the same no matter which side you choose.

Q: What does perpendicular height mean?

Perpendicular height means the height forms a 90° angle with the base. In this diagram, the dashed line from A straight down to the base BC shows the perpendicular height x.

Triangle Area Formula with Height Variable

Since the area of the triangle is equal to 15.

Find X.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:11 Let's find the height X of this triangle.

00:15 We'll use the triangle area formula, which you might remember from class.

00:20 The area equals base times height, divided by 2. Here, the base is BC, and the height is AE.

00:28 Now, let's plug in our values and solve for the height X.

00:32 To make our calculation easier, let's multiply both sides by 2 to get rid of fractions.

00:39 Next, we'll isolate X by itself to find our answer.

00:45 And there we have it! We've found the height X of our triangle.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Since the area of the triangle is equal to 15.

Find X.

Step-by-step solution

To solve for $x$ , let's apply the standard formula for the area of a triangle:

Given that the area $A = 15$ , base $b = 3$ , and height $h = x$ .

The area formula is:

$A = \frac{1}{2} \times b \times h$

Substituting the given values into the equation, we have:

$15 = \frac{1}{2} \times 3 \times x$

Now, simplify and solve for $x$ :

$15 = \frac{3}{2} \times x$

Multiply both sides by $\frac{2}{3}$ to isolate $x$ :

$x = 15 \times \frac{2}{3}$

Calculating, we obtain:

$x = \frac{30}{3} = 10$

Thus, the height $x$ of the triangle is $x = 10$ .

Therefore, the solution to the problem is $x = 10$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Area Formula: A = (1/2) × base × height for any triangle
Substitution: Replace known values: 15 = (1/2) × 3 × x
Check: Verify x = 10: (1/2) × 3 × 10 = 15 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by one-half
Don't use A = base × height = 3 × x = 45! This gives x = 5 which is wrong because you're using the rectangle formula instead of triangle. Always remember triangles need the (1/2) factor in the area formula.

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 triangles have that 1/2 in the area formula?

A triangle is exactly half of a rectangle! If you draw a rectangle with the same base and height, then draw a diagonal, you get two identical triangles. That's why we multiply by 1/2.

What if the triangle looks different from this one?

The formula $A = \frac{1}{2} \times base \times height$ works for any triangle! The height is always the perpendicular distance from the base to the opposite vertex.

How do I solve 15 = (3/2) × x step by step?

Multiply both sides by the reciprocal $\frac{2}{3}$ :

$15 \times \frac{2}{3} = x$
$\frac{30}{3} = 10$

Can I use a different side as the base?

Yes! You can pick any side as the base, but then the height must be perpendicular to that base. The area will always come out the same no matter which side you choose.

What does perpendicular height mean?

Perpendicular height means the height forms a 90° angle with the base. In this diagram, the dashed line from A straight down to the base BC shows the perpendicular height x.

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