Question

A triangle that has 3 acute angles is called a (acute triangle, obtuse triangle).
A garden in the shape of an equilateral triangle has sides whose lengths are 10 meters what is the area of the garden?
1) 25 m^2
2) 25 divided by 3 m^2
3) 50 m^2
4) 50 divided by 3 m^2

Answer 1

A triangle that has 3 acute angles is called an **acute triangle**.

To find the area of an equilateral triangle, we can use the formula:

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

where \( s \) is the length of a side of the triangle. In this case, the side length \( s \) is 10 meters.

Plugging in the value:

\[ \text{Area} = \frac{\sqrt{3}}{4} (10)^2 \]
\[ \text{Area} = \frac{\sqrt{3}}{4} \times 100 \]
\[ \text{Area} = 25\sqrt{3} \, \text{m}^2 \]

Now, to simplify or approximate \( 25\sqrt{3} \):
- The approximate value of \( \sqrt{3} \) is about 1.732.
- So, \( 25\sqrt{3} \approx 25 \times 1.732 \approx 43.3 \, \text{m}^2 \).

However, none of the specified answers in the question matches this. Upon review, it seems you have provided multiples of 25, which indicates the area will not be rationalized directly to a familiar whole number, but can be expressed based on angle measures.

However, I don't see \( 25\sqrt{3} \) listed among your options.

Given the choices provided, the best conclusion drawn is that **the area is closest to either \( 50/3 \, \text{m}^2 \) or a similar rational expression**. But **the exact area is \( 25\sqrt{3} \, m^2 \)** if we express it exactly.

If you were looking specifically for the computed area in a form, the option not directly listed among the choices could be the reasoning behind not simplifying to a precise option in the given context.