Find X in Right Triangle: Area 18.5 and Height 10 Units

Q: How do I know which side is the base and which is the height?

In a right triangle, the height is always perpendicular to the base. Look for the side that forms a 90° angle with another side - that's your height! The base is the side the height sits on.

Q: Why is there a ½ in the triangle area formula?

A triangle is exactly half of a rectangle! If you drew a rectangle with the same base and height, the triangle would take up exactly half the space, so we multiply by $ \frac{1}{2} $.

Q: What if I get a decimal answer - is that okay?

Yes, absolutely! Real-world measurements often result in decimal values. Just make sure to check your arithmetic and that your decimal makes sense in context.

Q: Can I use this formula for any triangle?

Yes! The formula $ A = \frac{1}{2} \times \text{base} \times \text{height} $ works for any triangle, not just right triangles. You just need to identify which side is your base and measure the perpendicular height to it.

Q: How do I solve for X when it's in the middle of the equation?

Use inverse operations! Since X is being multiplied, you'll need to divide to isolate it. Work step by step: first simplify $ \frac{1}{2} \times 10 = 5 $, then divide both sides by 5.

Triangle Area Formula with Given Measurements

Calculate X using the data in the figure below.

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Understand the problem

Calculate X using the data in the figure below.

Step-by-step solution

To find the missing side $X$ of the triangle:

Step 1: Identify the given values: area $A = 18.5$ and height $h = 10$ .
Step 2: Use the area formula for a triangle: $A = \frac{1}{2} \times \text{base} \times \text{height}$ .
Step 3: Plug in the known values into the formula:
$18.5 = \frac{1}{2} \times X \times 10$ .
Step 4: Simplify and solve for $X$ :
$18.5 = 5 \times X$
Divide both sides by 5 to isolate $X$ :
$X = \frac{18.5}{5}$ .
Step 5: Calculate $X$ :
$X = 3.7$ .

Therefore, the missing side $X$ is $3.7$ .

Final Answer

3.7

Key Points to Remember

Essential concepts to master this topic

Area Formula: Triangle area equals one-half times base times height
Technique: Substitute known values: $18.5 = \frac{1}{2} \times X \times 10$
Check: Verify by calculating: $\frac{1}{2} \times 3.7 \times 10 = 18.5$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to divide by 2 in the area formula
Don't use A = base × height = wrong answer that's twice as large! This ignores the crucial ½ factor in triangle area. Always remember the triangle area formula is $A = \frac{1}{2} \times \text{base} \times \text{height}$ .

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

How do I know which side is the base and which is the height?

In a right triangle, the height is always perpendicular to the base. Look for the side that forms a 90° angle with another side - that's your height! The base is the side the height sits on.

Why is there a ½ in the triangle area formula?

A triangle is exactly half of a rectangle! If you drew a rectangle with the same base and height, the triangle would take up exactly half the space, so we multiply by $\frac{1}{2}$ .

What if I get a decimal answer - is that okay?

Yes, absolutely! Real-world measurements often result in decimal values. Just make sure to check your arithmetic and that your decimal makes sense in context.

Can I use this formula for any triangle?

Yes! The formula $A = \frac{1}{2} \times \text{base} \times \text{height}$ works for any triangle, not just right triangles. You just need to identify which side is your base and measure the perpendicular height to it.

How do I solve for X when it's in the middle of the equation?

Use inverse operations! Since X is being multiplied, you'll need to divide to isolate it. Work step by step: first simplify $\frac{1}{2} \times 10 = 5$ , then divide both sides by 5.

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