Question

The Number System Unit Test 5 of 155 of 15 Items Question The height of an equilateral triangle equals 3√2 times the side length. Using 74 for the square root of 3, what is the approximate height in meters of an equilateral triangle with a side length of 8 meters?(1 point)

Answer 1

To find the height of an equilateral triangle when you know the side length, you can use the formula for the height \( h \) of an equilateral triangle:

\[
h = \frac{\sqrt{3}}{2} \times s
\]

where \( s \) is the side length.

In this case, the side length \( s \) is 8 meters. You mentioned that the height equals \( 3\sqrt{2} \) times the side length. However, it appears there may be some inconsistency because the height of the equilateral triangle is typically given as proportional to \( \sqrt{3} \).

Nevertheless, let’s calculate the height using both interpretations(3√2 and the standard formula).

1. **Using \( 3\sqrt{2} \)** times the side length:
\[
h = 3\sqrt{2} \times 8 = 24\sqrt{2}
\]
We will calculate \( h \) using an approximate value of \( \sqrt{2} \) (approximately 1.414):
\[
h \approx 24 \times 1.414 \approx 33.936 \text{ meters}
\]

2. **Using \( \frac{\sqrt{3}}{2} \)** times the side length:
\[
h = \frac{\sqrt{3}}{2} \times 8 = 4\sqrt{3}
\]
Now we substitute \( \sqrt{3} \) with 74:
\[
h \approx 4 \times 74 = 296 \text{ meters}
\]

If we based it on \( 3\sqrt{2} \), the height would be approximately 33.936 meters, while using the traditional formula with your value of \( \sqrt{3} \) would result in approximately 296 meters.

Please verify the specifics of the problem for clarity on which height calculation you require.