Triangle Area Problem: Finding Height X When Area = 15 and Base = 5

Q: Why do we use one-half in the triangle area formula?

A triangle is exactly half of a rectangle! If you draw a rectangle with the same base and height as your triangle, the triangle takes up exactly half the space.

Q: Which measurement is the base and which is the height?

The base can be any side of the triangle. The height is always the perpendicular distance from the opposite vertex to that base. In this problem, the base is 5 and height is x.

Q: What if I get a decimal answer instead of a whole number?

That's completely normal! Many triangle problems have decimal or fractional heights. Just make sure to substitute your answer back to verify it gives the correct area.

Q: How do I know if I'm using the right base and height?

The height must be perpendicular (at a 90° angle) to the base. In the diagram, you can see the height line forms a right angle with the base.

Triangle Area Formula with Height Calculation

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

00:00 Determine the height X

00:03 Apply the formula for calculating the area of a triangle

00:06 (base(BC) x height(AE)) divided by 2

00:14 Substitute in the relevant values and calculate to find height X

00:22 Multiply by 2 to avoid fractions

00:28 Isolate X

00:35 This is the solution

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 find $x$ , the vertical height of the triangle, we will use the area formula for a triangle:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

We know that:

The area of the triangle is 15.
The base of the triangle, $BE$ , is 5 units.
The height of the triangle, $AE$ , is $x$ units.

Substituting these values into the formula, we get:

$15 = \frac{1}{2} \times 5 \times x$

First, simplify the right side of the equation:

$15 = \frac{5}{2} \times x$

To isolate $x$ , multiply both sides by 2:

$30 = 5x$

Finally, divide both sides by 5 to solve for $x$ :

$x = \frac{30}{5} = 6$

Therefore, the value of $x$ is 6.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Area Formula: Area equals one-half times base times height
Technique: Substitute known values: $15 = \frac{1}{2} \times 5 \times x$
Check: Verify answer: $\frac{1}{2} \times 5 \times 6 = 15$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to use the one-half factor in area formula
Don't calculate Area = base × height = 5 × 6 = 30! This gives double the actual area because you forgot the ½ factor. Always remember that triangle area equals ½ × base × height, not just base × height.

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 we use one-half in the triangle area formula?

A triangle is exactly half of a rectangle! If you draw a rectangle with the same base and height as your triangle, the triangle takes up exactly half the space.

Which measurement is the base and which is the height?

The base can be any side of the triangle. The height is always the perpendicular distance from the opposite vertex to that base. In this problem, the base is 5 and height is x.

What if I get a decimal answer instead of a whole number?

That's completely normal! Many triangle problems have decimal or fractional heights. Just make sure to substitute your answer back to verify it gives the correct area.

How do I know if I'm using the right base and height?

The height must be perpendicular (at a 90° angle) to the base. In the diagram, you can see the height line forms a right angle with the base.

Can I solve this problem differently?

The area formula method is the most direct approach. You could also use other triangle area formulas, but $Area = \frac{1}{2} \times base \times height$ is perfect when you know the area and base.

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