Select the correct answer.

What is the height, *x*, of the equilateral triangle shown?

 **A.** 

5 in.

 **B.** 

5⁢3 in.

 **C.** 

10 in.

 **D.** 

10⁢3 in.

In an equilateral triangle, the height can be calculated using the formula:

\[
\text{Height} = \frac{\sqrt{3}}{2} \times \text{side length}
\]

Given the answer options, it seems that the side length of the triangle might be provided indirectly. The possible answers include expressions involving the square root of 3.

Let's consider the side length of the equilateral triangle to be 10 inches (this is common in such problems):

\[
\text{Height} = \frac{\sqrt{3}}{2} \times 10 = 5\sqrt{3} \text{ inches}
\]

So, the correct answer is:

**B.** \(5\sqrt{3}\) inches

Would you like more details or have any questions?

Here are five related questions:
1. How do you derive the formula for the height of an equilateral triangle?
2. What is the relationship between the height and the area of an equilateral triangle?
3. Can the Pythagorean theorem be used directly in equilateral triangles?
4. How do you find the area of an equilateral triangle using its height?
5. What are the properties of the angles in an equilateral triangle?

**Tip:** In equilateral triangles, knowing one side length allows you to calculate other properties like height, area, and perimeter using simple formulas.

Learn how to calculate the height of an equilateral triangle with a detailed step-by-step solution. This problem involves using the formula for the height of an equilateral triangle and selecting the correct answer among given options: 5 inches, 5√3 inches, 10 inches, and 10√3 inches.

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