Calculate Triangle Height X: Area 20 and Base 5 Problem

Q: Why do we multiply the area by 2 in this problem?

The triangle area formula is $ \text{Area} = \frac{\text{base} \times \text{height}}{2} $. To solve for height, we need to isolate it. First multiply both sides by 2 to eliminate the fraction!

Q: Which side of the triangle is the base and which is the height?

The base is any side you choose (here it's 5). The height is always the perpendicular distance from the opposite vertex to that base. Notice the small square symbol showing the 90° angle!

Q: How do I know if the triangle is a right triangle?

Look for the small square symbol at one of the corners - this shows a 90° angle. In this problem, angle A is the right angle, making AC perpendicular to AB.

Q: What if I get a decimal answer instead of 8?

Double-check your arithmetic! For this problem: $ 5x = 40 $, so $ x = 40 \div 5 = 8 $. The answer should be a whole number here.

Triangle Area Formula with Height Calculation

Calculate X using the data in the figure below.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine the value of X

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

00:06 (base x height) divided by 2

00:09 Substitute in the relevant values according to the given data and proceed to solve for X

00:13 Isolate X

00:16 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate X using the data in the figure below.

Step-by-step solution

The formula to calculate the area of a triangle is:

(side * height descending from the side) /2

We place the data we have into the formula to find X:

$20=\frac{AB\times AC}{2}$

$20=\frac{x\times5}{2}$

Multiply by 2 to get rid of the fraction:

$5x=40$

Divide both sections by 5:

$\frac{5x}{5}=\frac{40}{5}$

$x=8$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area = (base × height) ÷ 2 for any triangle
Technique: Rearrange to height = (2 × Area) ÷ base = (2 × 20) ÷ 5
Check: Substitute back: (5 × 8) ÷ 2 = 40 ÷ 2 = 20 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply area by 2 before dividing by base
Don't solve 20 = 5x ÷ 2 by just dividing 20 by 5 = wrong answer 4! This ignores the division by 2 in the area formula. Always multiply the area by 2 first: 5x = 40, then x = 8.

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 multiply the area by 2 in this problem?

The triangle area formula is $\text{Area} = \frac{\text{base} \times \text{height}}{2}$ . To solve for height, we need to isolate it. First multiply both sides by 2 to eliminate the fraction!

Which side of the triangle is the base and which is the height?

The base is any side you choose (here it's 5). The height is always the perpendicular distance from the opposite vertex to that base. Notice the small square symbol showing the 90° angle!

Can I use a different side as the base?

Yes! You can choose any side as the base, but then you must use the perpendicular height to that specific side. Different base = different height, but same area!

How do I know if the triangle is a right triangle?

Look for the small square symbol at one of the corners - this shows a 90° angle. In this problem, angle A is the right angle, making AC perpendicular to AB.

What if I get a decimal answer instead of 8?

Double-check your arithmetic! For this problem: $5x = 40$ , so $x = 40 \div 5 = 8$ . The answer should be a whole number here.

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