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

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

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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