Question

The area of an equilateral triangle is 187 centimeters squared.

Question
What is the approximate length of a side of the triangle?

Answer options with 5 options
A.
5.2 centimeters

B.
10.4 centimeters

C.
20.8 centimeters

D.
31.2 centimeters

E.
62.3 centimeters

Answer 1

To find the length of a side of an equilateral triangle given its area, we can use the formula for the area of an equilateral triangle:

\[
A = \frac{\sqrt{3}}{4} s^2
\]

where \( A \) is the area and \( s \) is the length of a side of the triangle.

Given that the area \( A = 187 \, \text{cm}^2 \), we can rearrange the formula to solve for \( s \):

\[
s^2 = \frac{4A}{\sqrt{3}}
\]

Substituting the area into the formula:

\[
s^2 = \frac{4 \times 187}{\sqrt{3}}
\]

Calculating this step by step:

1. Calculate \( 4 \times 187 \):

\[
4 \times 187 = 748
\]

2. Now divide by \( \sqrt{3} \) (approximately 1.732):

\[
s^2 \approx \frac{748}{1.732} \approx 432.158
\]

3. Finally, take the square root to find \( s \):

\[
s \approx \sqrt{432.158} \approx 20.8 \, \text{cm}
\]

Thus, the approximate length of a side of the triangle is \( 20.8 \, \text{centimeters} \).

The correct answer is **C. 20.8 centimeters**.