Find X in a Right Triangle: Given Area 8.375 and Height 2.5

Q: Why do I multiply by 2 in the calculation?

When you rearrange the area formula $ A = \frac{1}{2} \times b \times h $ to solve for a missing side, you need to isolate that side. Multiplying both sides by 2 cancels out the fraction ½.

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

In a right triangle, any of the two perpendicular sides can be considered base and height. The important thing is that they form the 90° angle, not which one you call base or height.

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

Absolutely! Decimal answers are very common in geometry problems. Just make sure to double-check your arithmetic and verify by substituting back into the area formula.

Q: Can I use this method for any triangle?

This specific area formula $ A = \frac{1}{2} \times b \times h $ works for any triangle when you know the base and the perpendicular height to that base, not just right triangles!

Q: What if the area or measurements were given as fractions?

The same process works! Just be extra careful with your fraction arithmetic. Convert to decimals if it makes the calculation easier, then convert back if needed.

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

00:12 Isolate X

00:21 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Calculate X using the data in the figure below.

2

Step-by-step solution

To solve this problem, let's follow these steps:

Step 1: Identify the given information: The area $A = 8.375$ , one side $a = X$ , and the other side $b = 2.5$ .
Step 2: Utilize the formula for the area of a right triangle, $A = \frac{1}{2} \times \text{base} \times \text{height}$ .
Step 3: Plug in the known values to the formula and solve for $X$ .

Detailed solution:

We have the area formula for a right triangle:

A = \frac{1}{2} \times X \times 2.5

Substitute the given area value:

8.375 = \frac{1}{2} \times X \times 2.5

Let's rearrange this equation to solve for $X$ :

X = \frac{8.375 \times 2}{2.5}

Calculate:

X = \frac{16.75}{2.5} = 6.7

Therefore, the length of side $X$ is $\mathbf{6.7}$ .

This corresponds to choice 2: 6.7

3

Final Answer

6.7

Key Points to Remember

Essential concepts to master this topic

Area Formula: Right triangle area equals half base times height
Technique: Rearrange $A = \frac{1}{2} \times b \times h$ to solve for unknown side
Check: Verify $\frac{1}{2} \times 6.7 \times 2.5 = 8.375$ ✓

Common Mistakes

Avoid these frequent errors

Using wrong area formula or forgetting the half
Don't calculate Area = base × height = 6.7 × 2.5 = 16.75! This gives double the correct area because you forgot the ½. Always remember that triangle area equals ½ × base × height, not just base × 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

Why do I multiply by 2 in the calculation?

+

When you rearrange the area formula $A = \frac{1}{2} \times b \times h$ to solve for a missing side, you need to isolate that side. Multiplying both sides by 2 cancels out the fraction ½.

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

+

In a right triangle, any of the two perpendicular sides can be considered base and height. The important thing is that they form the 90° angle, not which one you call base or height.

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

+

Absolutely! Decimal answers are very common in geometry problems. Just make sure to double-check your arithmetic and verify by substituting back into the area formula.

Can I use this method for any triangle?

+

This specific area formula $A = \frac{1}{2} \times b \times h$ works for any triangle when you know the base and the perpendicular height to that base, not just right triangles!

What if the area or measurements were given as fractions?

+

The same process works! Just be extra careful with your fraction arithmetic. Convert to decimals if it makes the calculation easier, then convert back if needed.

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Find X in a Right Triangle: Given Area 8.375 and Height 2.5

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